SYSTEMS AND METHODS FOR APPROXIMATING MUSCULOSKELETAL DYNAMICS

Abstract

A system and method for controlling a device, such as a prosthetic limb are provided. A biomimetic controller of the system comprises a signal processor and a musculoskeletal model. The signal processor processes M biological signals received from a residual limb to transform the M biological signals into N activation signals, where M and N are integers and M is less than N. The musculoskeletal model transforms the N activation signals into intended motion signals. A prosthesis controller transforms the intended motion signals into three or more control signals that are outputted from an output port of the prosthesis controller. A controlled device receives the control signals and performs one or more tasks in accordance with the control signals.

Claims

1. A system comprising: a controller comprising a processor and a memory; and machine-readable instructions stored in the memory that, when executed by the processor, cause the controller to at least: receive at least one biological signal from a residual limb; expand the at least one biological signal into one or more activation signals based at least in part on a polynomial associated with musculoskeletal dynamics of the residual limb; transform the one or more activation signals into one or more intended motion signals based at least in part on a plurality of approximated muscle dynamics; and transform the one or more intended motion signals into one or more control signals.

2. The system of claim 1, further comprising: a controlled device in communication with the controller; and wherein execution of the machine-readable instructions further cause the controller to at least send the one or more control signals to the controlled device.

3. The system of claim 2, wherein the controlled device comprises an active assistive device selected from a group consisting of an exoskeleton system and a muscle stimulation system.

4. The system of claim 2, wherein the controlled device comprises a computer interface device selected from a group consisting of a gaming controller system, a gesture-based interactive system, a drone, and a robot.

5. The system of claim 1, wherein execution of the machine-readable instructions cause the controller to expand the at least one biological signal into one or more activation signals, and further cause the controller to at least: receive an input dataset associated with muscle length and moment arms corresponding to the residual limb; generate at least one approximation polynomial based at least in part on the input dataset; and expand the at least one biological signal into one or more activation signals based at least in part on the approximation polynomial.

6. The system of claim 5, wherein execution of the machine-readable instructions further cause the controller to at least: generate a candidate list of terms for expanding the approximation polynomial; expand the approximation polynomial by a best candidate term from the candidate list of terms to yield an expanded approximation polynomial; and approximate the musculoskeletal dynamics of the residual limb based at least in part on the expanded approximation polynomial.

7. A method for controlling a device comprising: receiving, by a controller, at least one biological signal from a residual limb; expanding, by the controller, the at least one biological signal into one or more activation signals based at least in part on a polynomial associated with musculoskeletal dynamics of the residual limb; transforming, by the controller, the one or more activation signals into one or more intended motion signals based at least in part on a plurality of approximated muscle dynamics; and transforming, by the controller, the one or more intended motion signals into one or more control signals.

8. The method of claim 7, further comprising at least: receiving, by the controller, an input dataset associated with muscle length and moment arms corresponding to the residual limb; generating, by the controller, at least one approximation polynomial based at least in part on the input dataset; and expanding, by the controller, the at least one biological signal into one or more activation signals based at least in part on the approximation polynomial.

9. The method of claim 7, further comprising at least: generating, by the controller, a candidate list of terms for expanding the approximation polynomial; expanding, by the controller, the approximation polynomial by a best candidate term from the candidate list of terms to yield an expanded approximation polynomial; and approximating, by the controller, the musculoskeletal dynamics of the residual limb based at least in part on the expanded approximation polynomial.

10. The method of claim 7, further comprising sending, by the controller, the one or more control signals to a controlled device.

11. The method of claim 10, wherein the controlled device comprises an active assistive device selected from a group consisting of an exoskeleton system and a muscle stimulation system.

12. The method of claim 10, wherein the controlled device comprises a computer interface device selected from a group consisting of a gaming controller system, a gesture-based interactive system, a drone, and a robot.

13. A system comprising: a controller comprising a processor, the controller configured to at least: receive at least one biological signal from a residual limb; execute a signal processing algorithm to expand the at least one biological signal into one or more activation signals based at least in part on a polynomial associated with musculoskeletal dynamics of the residual limb; execute a modeling algorithm to transform the one or more activation signals into one or more intended motion signals based at least in part on a plurality of approximated muscle dynamics; and execute a control algorithm to transform the one or more intended motion signals into one or more control signals.

14. The system of claim 13, further comprising: a controlled device in communication with the controller; and wherein the controller is further configured to at least send the one or more control signals to the controlled device.

15. The system of claim 14, wherein the controlled device comprises an active assistive device selected from a group consisting of an exoskeleton system, a muscle stimulation system, and a prosthetic limb.

16. The system of claim 14, wherein the controlled device comprises a computer interface device selected from a group consisting of a gaming controller system, a gesture-based interactive system, a drone, and a robot.

17. The system of claim 13, wherein executing the signal processing algorithm further causes the controller to at least: receive an input dataset associated with muscle length and moment arms corresponding to the residual limb; generate at least one approximation polynomial based at least in part on the input dataset; and expand the at least one biological signal into one or more activation signals based at least in part on the approximation polynomial.

18. The system of claim 17, wherein executing the signal processing algorithm further causes the controller to at least: generate a candidate list of terms for expanding the approximation polynomial; expand the approximation polynomial by a best candidate term from the candidate list of terms to yield an expanded approximation polynomial; and approximate the musculoskeletal dynamics of the residual limb based at least in part on the expanded approximation polynomial.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0012] FIG. 1 is an OpenSim model of an upper limb of a human arm having various musculotendon actuators.

[0013] FIGS. 2A and 2B are plots of kinematic variables in terms of muscle length versus (vs.) radians and moment arm vs. radians, respectively, for the extensor carpi ulnaris muscle in different positions of wrist extension-flexion (e-f) and supination-pronation (s-p) degrees of freedom (DOFs).

[0014] FIG. 3 is a flow diagram representing the approximation method performed by a processor in accordance with a representative embodiment.

[0015] FIG. 4 is a flow diagram representing the approximation method in accordance with a preferred embodiment in which the muscle length polynomial and the moment arm polynomials are constrained by a relationship that exists between muscle length and associated moment arms.

[0016] FIG. 5 is a graph showing iteration of the approximation method represented by the flow diagram of FIG. 4 vs. the precision of the fit obtained by the method.

[0017] FIGS. 6A and 6B illustrate histograms of the normalized error in estimation of muscle lengths and moment arms, respectively, using splines and optimized polynomials with and without the aforementioned constraint associated with steps 11-13 of FIG. 4.

[0018] FIG. 7A illustrates a graph of similarity index (SI) between polynomials composed with and without the differential relationship between length and moment arms of each muscle, which illustrates that the compositions are similar.

[0019] FIG. 7B illustrates a graph of the number of joints the muscle spans vs. the number of terms in the approximating polynomials, which demonstrates that the number of terms increases with the number of joints the muscle spans.

[0020] FIG. 8A shows an average-linkage dendrogram and the heatmap of distances between muscle vectors in the space defined by the polynomial terms that are independent of DOF identity.

[0021] FIG. 8B shows all muscle vectors in the axes of the two first principle components: x-axis represents linear (x) terms and y-axis represents quadratic (x.sup.2) terms.

[0022] FIG. 9A is a graph showing two probability density distributions of muscle vector distances for muscles with and without shared anatomical DOFs. The asterisks indicate p<10.sup.?8 in statistical comparisons with ?=0.05.

[0023] FIG. 9B is a graph showing the difference between the distributions in FIG. 9A. The asterisk indicates p<10.sup.?8 in a statistical comparison to zero with ?=0.05.

[0024] FIG. 9C is a graph showing two probability density distributions of muscle vector distances for muscles sharing spanning at least one the same DOF and belonging to two different functional groups, e.g., flexors and extensors.

[0025] FIG. 9D is a graph showing the difference between the distributions in FIG. 9C.

[0026] FIG. 10 is a block diagram of a system in accordance with a representative embodiment that enables biomimetic processing of biological inputs in order to control an actual prosthesis device.

[0027] FIG. 11 illustrates a dendrogram that shows the transformations inside the signal processor shown in FIG. 10 and lists acronyms corresponding to a set of N simulated activation signals that are generated from a subset of M available biological signals based on the illustrated dendrogram.

[0028] FIG. 12 is a block diagram showing the system in accordance with a representative embodiment that enables biomimetic processing of biological inputs in order to generate control signals for controlling a virtual reality (VR) prosthesis system.

[0029] FIG. 13 is a block diagram of the system in accordance with an embodiment that combines the features of the systems shown in FIGS. 10 and 12 to enable biomimetic processing of biological inputs in order to generate control signals for controlling the VR prosthesis system or the prosthesis device.

[0030] FIG. 14 is a flow diagram depicting the method in accordance with a representative embodiment.

[0031] FIG. 15 is a flow diagram of modifications to the method represented by the flow diagram of FIG. 14 for the case where the controlled device referred to in step 144 is a VR prosthesis system or a prosthetic limb.

[0032] FIG. 16 is a flow diagram of modifications to the method represented by the flow diagram of FIG. 15 in accordance with an embodiment.

[0033] FIG. 17 is a flow diagram of modifications to the method represented by the flow diagram of FIG. 16 in accordance with an embodiment.

[0034] FIGS. 18A-18C are graphs demonstrating multi-dimensional control of a controlled device, e.g., a prosthetic limb, by the systems shown in FIGS. 10, 12 and 13 in accordance with a representative embodiment.

DETAILED DESCRIPTION

[0035] Representative embodiments of the present disclosure are directed to various embodiments of a system and method for controlling a device, such as a virtual reality (VR) and/or a prosthetic limb. In accordance with an embodiment, a biomimetic controller of the system comprises a signal processor and a musculoskeletal model. The signal processor processes M biological signals received from a residual limb to transform the M biological signals into N activation signals, where M and N are integers and M is less than N. The musculoskeletal model transforms the N activation signals into intended motion signals. A prosthesis controller transforms the intended motion signals into control signals that are outputted from an output port of the prosthesis controller. A controlled device receives the control signals and performs one or more tasks in accordance with the control signals.

[0036] The above-referenced PCT international application number PCT/US2008/051575 (hereinafter referred to as the parent application), which is the parent application of the present application, discloses, inter alia, an approximation method that includes the steps of acquiring or receiving an input dataset associated with muscle lengths and moment arms for a plurality of physiological postures of a body limb, preselecting respective polynomials that approximate the muscle moment arms and lengths, generating respective lists of one or more candidates for expanding each respective polynomial, selecting a respective candidate for expanding each polynomial based on respective estimates of which of the candidates is the most suitable candidate, expanding the respective polynomials by the respective selected candidates, determining whether further expansion of the polynomials is possible and would be sufficiently beneficial to warrant expansion. If so, the process returns to the step of generating respective lists of candidates for expansion followed by the step of selecting the respective suitable candidates. If not, the musculoskeletal dynamics of the limb are estimated based on the latest structure of the polynomials.

[0037] In accordance with a preferred embodiment, the approximation method disclosed in the parent application is performed to obtain the structures of the polynomials a priori. Then, in accordance with embodiments disclosed herein, the polynomial structures obtained are used in a biomimetic controller to estimate musculoskeletal dynamics in real-time or near-real time in order to simultaneously control multiple DOFs of some device, such as a real prosthesis device, for example.

[0038] For completeness, prior to describing representative embodiments in accordance with the inventive principles and concepts of the present disclosure, portions of the parent application are repeated herein with reference to FIGS. 1-9D of the parent application. Then, representative embodiments according to teachings of the present disclosure are described herein with reference to FIGS. 10-18C.

[0039] In the following detailed description, for purposes of explanation and not limitation, example embodiments disclosing specific details are set forth in order to provide a thorough understanding of an embodiment according to the present teachings. However, it will be apparent to one having ordinary skill in the art having the benefit of the present disclosure that other embodiments according to the present teachings that depart from the specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known apparatuses and methods may be omitted so as to not obscure the description of the example embodiments. Such methods and apparatuses are clearly within the scope of the present teachings.

[0040] The terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting. The defined terms are in addition to the technical and scientific meanings of the defined terms as commonly understood and accepted in the technical field of the present teachings.

[0041] As used in the specification and appended claims, the terms a, an, and the include both singular and plural referents, unless the context clearly dictates otherwise. Thus, for example, a device includes one device and plural devices.

[0042] Relative terms may be used to describe the various elements' relationships to one another, as illustrated in the accompanying drawings. These relative terms are intended to encompass different orientations of the device and/or elements in addition to the orientation depicted in the drawings.

[0043] It will be understood that when an element is referred to as being connected to or coupled to or electrically coupled to another element, it can be directly connected or coupled, or intervening elements may be present.

[0044] The term memory or memory device, as those terms are used herein, are intended to denote a non-transitory computer-readable storage medium that is capable of storing computer instructions, or computer code, for execution by one or more processors or controllers. References herein to memory or memory device should be interpreted as one or more memories or memory devices. The memory may, for example, be multiple memories within the same computer system. The memory may also be multiple memories distributed amongst multiple computer systems or computing devices.

[0045] A controller, as that term is used herein, encompasses an electronic component that is able to execute a computer program or executable computer instructions. A controller may also refer to a collection of controllers. A controller may comprise one or more processors, such as, for example, a microprocessor or microcontroller.

[0046] Exemplary, or representative, embodiments will now be described with reference to the figures, in which like reference numerals represent like components, elements or features. It should be noted that features, elements or components in the figures are not intended to be drawn to scale, emphasis being placed instead on demonstrating inventive principles and concepts.

[0047] For purposes of demonstrating the inventive principles and concepts, the systems and methods will be described with reference to approximating complex musculoskeletal dynamics of the right arm and hand of a human being. However, persons of skill in the art will understand, in view of the description provided herein, that the systems and methods described herein can be used to approximate the musculoskeletal dynamics of any anatomical feature.

[0048] FIG. 1 is an OpenSim model 1 of a human right arm and hand showing the geometry of muscle paths as straight and curved lines over the skeletal structure for the displayed posture. The model 1, which is defined by the values shown in Tables 1 and 2 below for the limb shown in FIG. 1, is a known model that was previously developed to capture the relationship between muscle lengths and moment arms in all physiological postures. The model 1 contains a plurality of muscles described with a plurality of musculotendon actuators. The values for the corresponding kinematic variables were obtained on a uniform grid with nine points per DOF, resulting in the domain size of 9.sup.d data points per muscle, where d is the number of DOFs that a muscle crosses. For example, since the extensor carpi ulnaris muscle spans two DOFs (wrist flexion-extension and pronation-supination), its moment arms and muscle lengths were sampled in 9.sup.2=81 positions.

TABLE-US-00001 TABLE 1 id Name Range, rad Description 1 ra_wr_s_p ?1.5708 1.5708 wrist pronation/ supination motion 2 ra_wr_e_f ?1.2217 1.2217 wrist flexion/ extension motion 3 ra_cmc1_f_e 0 0.8727 thumb proximal flexion/ extension motion 4 ra_cmc1_ad_ab 0 0.8727 thumb proximal abduction/ adduction motion 5 ra_mcp1_f_e ?0.7854 0 thumb central flexion/ extension motion 6 ra_ip1_f_e ?1.5708 0 thumb distal flexion/ extension motion 7 ra_mcp2_e_f 0 1.5708 index proximal flexion/ extension motion 8 ra_pip2_e_f 0 2.0944 index central flexion/ extension motion 9 ra_dip2_e_f 0 1.5708 index distal flexion/ extension motion 10 ra_mcp3_e_f 0 1.5708 middle proximal flexion/ extension motion 11 ra_pip3_e_f 0 2.0944 middle central flexion/ extension motion 12 ra_dip3_e_f 0 1.5708 middle distal flexion/ extension motion 13 ra_mcp4_e_f 0 1.5708 ring proximal flexion/ extension motion 14 ra_pip4_e_f 0 2.0944 ring central flexion/ extension motion 15 ra_dip4_e_f 0 1.5708 ring distal flexion/ extension motion 16 ra_mcp5_e_f 0 1.5708 pinky proximal flexion/ extension motion 17 ra_pip5_e_f 0 2.0944 pinky central flexion/ extension motion 18 ra_dip5_e_f 0 1.5708 pinky distal flexion/ extension motion 19 ra_el_e_f 0 2.2689 elbow flexion/ extension motion The list of simulated DOFs. The last two suffixes separated by underscores indicate the direction of the motion, e.g., s_p indicates the motion from supinated to pronated posture.

TABLE-US-00002 TABLE 2 id Name Full name DOFs 1 BIC_LO Biceps brachii long 19 1 head 2 BIC_SH Biceps brachii short 19 1 head 3 BRR Brachioradialis 19 1 4 SUP Supinator 1 5 PT Pronator teres 1 6 PQ Pronator quadratus 1 7 ECR_LO Extensor carpi radialis 1 2 longus 8 ECR_BR Extensor carpi radialis 1 2 brevis 9 ECU Extensor carpi ulnaris 1 2 10 FCR Flexor carpi radialis 1 2 11 FCU Flexor carpi ulnaris 1 2 12 PL Palmaris longus 1 2 13 FDS5 Flexor digitorum 2 16 17 superficialis (pinky finger) 14 FDS4 Flexor digitorum 2 13 14 superficialis (ring finger) 15 FDS3 Flexor digitorum 2 10 11 superficialis (middle finger) 16 FDS2 Flexor digitorum 2 7 8 superficialis (index finger) 17 FDP5 Flexor digitorum 2 16 17 18 profundus (pinky finger) 18 FDP4 Flexor digitorum 2 13 14 15 profundus (ring finger) 19 FDP3 Flexor digitorum 2 10 11 12 profundus (middle finger) 20 FDP2 Flexor digitorum 2 7 8 9 profundus (index finger) 21 EDM Extensor digiti minimi 2 16 17 18 22 ED5 Extensor digitorum 2 16 17 18 (pinky finger) 23 ED4 Extensor digitorum 2 13 14 15 (ring finger) 24 ED3 Extensor digitorum 2 10 11 12 (middle finger) 25 ED2 Extensor digitorum 2 7 8 9 (index finger) 26 EIND Extensor indicis 2 7 8 9 27 EPL Extensor pollicis 1 2 4 3 5 6 longus 28 EPB Extensor pollicis 2 4 3 5 brevis 29 FPB Flexor pollicis brevis 4 3 5 30 FPL Flexor pollicis longus 2 4 3 5 6 31 APL Abductor pollicis 1 2 4 3 longus 32 OP Opponens pollicis 4 3 33 APB Abductor pollicis 4 3 5 brevis 34 ADPT Adductor pollicis 4 3 5 transversus The list of simulated muscles. The list of DOFs that each muscle spans is shown with the list of id values from the previous table.

[0049] To compare quality for the approximations with different known methods that are described below, a dataset (total 1,023,474 points) was used that combined the points used for the creation of the models (675,162, grid of 9 points per DOF per muscle), and an additional test dataset between the fitting data (348,312, grid of 8 points per DOF per muscle).

[0050] The aforementioned preselected polynomials that approximate the muscle moment arms and lengths have the polynomial structure given by Equation 1:

[00001]$\begin{array}{cc}f\left(x\right)=a+{.Math.}_p^{?}{.Math.}_{i_1?i_2?.Math.?i_p}^d{M}_{i_{1,}{i}_{2,.Math.,}{i}_p}{.Math.}_j^p{x}_{i_j}& \mathrm{Equation}1\end{array}$

where a is an intercept, ? is the user-selected maximum of polynomial power, d is the number of DOFs, x=(x.sub.1, . . . , x.sub.d).sup.T is the state vector for each DOF, M is the multidimensional matrix of polynomial terms, and indices in sums and product start at 1. The non-zero values of M and the intercept define the polynomial structure. For example, extensor carpi ulnaris moment arms are described by (a, M.sub.0, M.sub.1, M.sub.00, M.sub.01, M.sub.11, M.sub.000, M.sub.001, M.sub.011, M.sub.111) around elbow flexion-extension, and (a, M.sub.0, M.sub.00, M.sub.01, M.sub.11, M.sub.000, M.sub.001, M.sub.011, M.sub.111) around wrist pronation-supination, where index 0 is pronation-supination and 1 is flexion-extension. Values for these non-zero elements were obtained using a known linear pseudoinverse, such as, for example, the Moore-Penrose inverse. As will be described below in more detail, in accordance with a preferred embodiment, terms are added to the polynomial structure given by Equation 1 as needed to improve the approximation, but in a way that greatly reduces the amount of time and resources required to perform the approximation computations.

[0051] FIGS. 2A and 2B contain plots 2-4 of kinematic variables in terms of muscle length versus (vs.) radians and moment arm vs. radians, respectively, for the extensor carpi ulnaris muscle in different positions of wrist extension-flexion (e-f) and supination-pronation (s-p) DOFs. The points in FIGS. 2A and 2B correspond to the approximated data. The accuracy of polynomial fit generally increases as the number of terms in the polynomial structure increases. A list of polynomials that contain one more term than a preselected polynomial P(x) will be referred to herein as the list of potential candidates ?(P(x)) for expansion of the preselected polynomial. Each element of this list is a polynomial with the structure of P(x), but having one additional term that is present in the full polynomial of the correct power and dimensionality, but lacking in P(x). The number of elements in the list equals the number of elements that are present in the full polynomial but lacking in P(x). For example, let P(x) be a two-dimensional polynomial with structure (a, M.sub.0, M.sub.00), full two-dimensional (2-D) polynomial of power 2 has a structure (a, M.sub.0, M.sub.1, M.sub.00, M.sub.01, M.sub.11). Then the list of potential candidates is: ?(P(x))=[(a, M.sub.0, M.sub.1, M.sub.00); (a, M.sub.0, M.sub.00, M.sub.01); (a, M.sub.0, M.sub.00, M.sub.11)].

[0052] FIG. 3 is a flow diagram representing the approximation method performed by a processor or controller in accordance with a representative embodiment. For ease of discussion, the approximation method represented by the flow diagram will be described with reference to polynomials associated with a muscle length and the moment arms of a single muscle for a plurality of limb postures. For this example, it will be assumed that there are two moment arms associated with the muscle. In other words, for this example, the muscle crosses two DOFs. Therefore, the method will use a first polynomial associated with the muscle length and first and second polynomials associated with first and second moment arms, respectively. It should be understood, however, that for a given limb being modeled, the method represented by the flow diagram may be performed for one or more muscles of the limb, for one or more limb postures, for one or more muscle lengths and for the associated moment arms, depending on the application. For example, it may not be necessary to perform the method for all muscles of the right arm and the associated muscle lengths and moment arms if the model is being used to control a right hand prosthetic. The range of simulation can be represented by a single posture or by the full range of postures.

[0053] With reference to FIG. 3, an input dataset associated with the muscle length and the two moment arms is received in the processor, as indicated by block 11. The input dataset is used to generate a first polynomial having a preselected structure that approximates the muscle length and first and second polynomials associated with the corresponding moment arms, as indicated by block 12. The preselected structure is an empty list in the beginning, and a polynomial starts without any terms. For each of the polynomials, a list of one or more candidates for expanding the polynomial structure by at least one additional term is generated, as indicated by block 13. For each of the polynomials, one of the candidates on the respective list is selected for expanding the respective polynomial structure based on a respective determination of which of the candidates on the respective list is the most suitable candidate, as indicated by block 14. Each polynomial structure is then expanded by the respective selected candidate, as indicated by block 15. For each expanded polynomial, a determination is made as to whether further expansion of the polynomial structure is possible, and if so, whether expansion would be sufficiently beneficial to warrant expansion, as indicated by block 16. If so, the process returns to block 13. If not, the musculoskeletal dynamics of the limb are estimated based on the current structures of the polynomials obtained at block 15, as indicated by block 17.

[0054] In accordance with a preferred embodiment, the approximation method is constrained by a known relationship that exists between muscle length and the associated moment arms, which is given below by Equation 2. Moment arms can be estimated as a partial differential of the associated muscle length in local coordinates as:

[00002]$\begin{array}{cc}{M}_i\left(x\right)=\frac{?L\left(x\right)}{?x_i}& \mathrm{Equation}2\end{array}$

where i is the index of a DOF actuated by the muscle, x.sub.i is the coordinate of DOF i, M.sub.i(x) is the posture-dependent function of the muscle's moment arm around DOF i, L(x) is the function of muscle length. In accordance with a preferred embodiment, the relationship expressed by Equation 2 is used to constrain the polynomial terms used in the approximation functions for the kinematic variables (P.sub.L(x), {P.sub.Mi(x)}), as will now be described with reference to FIG. 4.

[0055] FIG. 4 is a flow diagram representing the approximation method in accordance with the preferred embodiment in which the muscle length polynomial and the moment arm polynomials are constrained by the relationship expressed by Eq. 2. The approximation method is identical to the approximation method represented by the flow diagram shown in FIG. 3 except that additional steps represented by blocks 21-23 in FIG. 4 are performed to constrain the polynomials in accordance with the relationship expressed by Eq. 2. As will be described below in more detail, constraining the polynomials allows the polynomial structures to be optimized, or at least improved, at very high speed, which greatly reduces the overall amount of time that is required to perform the computations.

[0056] With reference to FIG. 4, after each polynomial structure has been expanded by the respective selected candidate at the step represented by block 15, the moment arm polynomials are integrated, as indicated by block 21. This process can be expressed as: calculate {P.sub.Li=?P.sub.Midx.sub.i}. The integrals are then joined with the expanded muscle length polynomial, as indicated by block 22. This process can be expressed as: P.sub.L or P.sub.Li:L=P.sub.LU(U.sub.iP.sub.Li). The step of joining the integrals with the expanded muscle length polynomial results in a new muscle length polynomial having each term that is present in the integrals and in the expanded muscle length polynomial and having coefficients for the terms that are recalculated using the input dataset obtained at block 11 that the approximation method is attempting to fit. The new muscle length polynomial, L(x), obtained at the step represented by block 22 is then differentiated at the step represented by block 23 to produce new moment arm polynomials, M.sub.i(x). This process can be expressed as:

[00003]$\left\{M_i\left(x\right)=\frac{\mathrm{dL}\left(x\right)}{{\mathrm{dx}}_i}\right\}.$

[0057] For example, let x=(x.sub.1, x.sub.2), P.sub.L=2x.sub.1x.sub.2.sup.2, P.sub.M1=3x.sub.1.sup.3+2, P.sub.M2=5x.sub.1x.sub.2. Then P.sub.L1=x.sub.1.sup.4+2x.sub.1+const, P.sub.L2=2.5x.sub.1x.sub.2.sup.2+const. And the resulting polynomial functions adhering to Eq. 2 are: L=C.sub.0+C.sub.1x.sub.1x.sub.2.sup.2+C.sub.2x.sub.1.sup.4+C.sub.3x.sub.1, M.sub.1=C.sub.4x.sub.2.sup.2+C.sub.5x.sub.1.sup.3+C.sub.6, M.sub.2=C.sub.7x.sub.1x.sub.2, where coefficients C.sub.0-7 are calculated using the original dataset and a linear pseudoinverse. Similarly, it can be easily described using structures: P.sub.L:(M.sub.122), P.sub.M1:(a, M.sub.111), P.sub.M2:(M.sub.12); therefore P.sub.L1:(a, M.sub.1, M.sub.1111), P.sub.M2:(a, M.sub.122); and so L:(a, M, M.sub.122, M.sub.1111), M.sub.1:(a, M.sub.22, M.sub.111), M.sub.2(M.sub.12).

[0058] The process then continues to the step represented by block 16 described above with reference to FIG. 3. Muscle paths vary greatly in their complexity, from the simplest, which barely change with posture and can be approximated with a constant, to very complex that require many polynomial terms. To choose the best polynomial structure, one ought to test each one and choose the best. The number of possible structures representing a muscle across physiological postures grows exponentially with the number of DOFs that a muscle crosses. In accordance with a preferred embodiment, the steps represented by blocks 14-16 comprise an optimization algorithm that is based on forward stepwise regression and that gradually expands the polynomial structures by adding more terms as long as a determination is made at block 16 that the information tradeoff is beneficial, and it is possible to expand the polynomial structures. The information tradeoff is expressed as the corrected Akaike Information Criterion (AICc, Equation 3), which is a correction of Akaike Information Criterion for a finite sample size to avoid overfitting. The lower new value of AICc corresponds to the beneficial choice where a new polynomial approximates the data with higher precision using less variables, higher precision and using the same number of variables, the same precision using less variables, and in some other more complex cases. In accordance with this embodiment, the optimization algorithm compares the models corresponding to the polynomials of the listed expanded potential candidates to one another and chooses the best (the one with the lowest AICc). That model, it turn, is compared to the model created in the previous iteration.

[00004]$\begin{array}{cc}\mathrm{AICc}\left(f\right)=\mathrm{AIC}\left(f\right)+\frac{2k\left(k+1\right)}{N-k-1}=2k-2\ln \left(L\right)+\frac{2k\left(k+1\right)}{N-k-1}& \mathrm{Equation}3\end{array}$

where f is the approximation function, AIC is the Akaike Information Criterion, k is the number of parameters in the model, N is the number of data points, and L is the maximum likelihood of the polynomial representing this dataset.

[0059] For demonstrative purposes, the AIC calculation assumes a normal distribution of residuals and is based on normalized root means squared

[00005]$\begin{array}{cc}\left(\mathrm{RMS}={\left(\frac{\mathrm{RSS}}{N}\right)}^{0.5}\right):\mathrm{AICc}\left(f\right)=2k+2N\ln \left(\mathrm{RMS}\right)+\frac{2k\left(k+1\right)}{N-k-1}& \mathrm{Equation}4\end{array}$

The kinematic variables are normalized to preserve consistency in term N.Math.ln(RMS) across DOFs. Muscle lengths are normalized to the range of motion, and moment arms are normalized to the maximum magnitude across postures. If all functions cannot expand anymore (length of ?(F) is zero) or if the AICc did not improve in the current iteration, the approximation performs the step represented by block 17 and finishes.

[0060] FIG. 5 is a graph 31 showing iteration of the approximation method represented by the flow diagram of FIG. 4 vs. the precision of the fit obtained by the method. The graph 31 shows the progression of the algorithm and optimization of kinematic variables of a single muscle (flexor pollicis longus) and the added terms after each iteration. After the first iteration, the muscle length is approximated by (a, M.sub.1, M.sub.2, M.sub.4, M.sub.5, M.sub.33), an intercept a was added in the step represented by block 15 for P L , other terms came from the step represented by block 21 (from integration of moment arms polynomials). In the second iteration, the approximation expands using elements M.sub.11, M.sub.44, M.sub.55, M.sub.111, M.sub.333, M.sub.2222, and the precision of muscle length fit decreases below 1% (black line). In the fifth iteration, the moment arms around wrist extension-flexion, thumb MCP flexion and thumb DIP flexion have reached the minimum of AICc and were not improved any more. In the seventh iteration, the optimization of remaining kinematic parameters is finished.

[0061] The inventors identified how similar the muscles' structures obtained were with adherence to Eq. 2 (flow diagram of FIG. 4) and without adherence to Eq. 2 (flow diagram of FIG. 3). This difference was assessed using a similarity index (SI) that counted common elements in both structures. Structures of polynomials L.sub.A and L.sub.B corresponding to lengths of two muscles, muscles A and B, respectively, can be represented as: L.sub.A=P.sub.CUP.sub.ANC, L.sub.B=P.sub.CUP.sub.BNC, where P.sub.C is the shared structure of terms between L.sub.A and L.sub.B; P.sub.ANC and P.sub.BNC are the non-common polynomial structures of terms present in A and not in B, and vice versa. Then, the similarity index is stated as:

[00006]$\begin{array}{cc}\mathrm{SI}\left(A,B\right)=\frac{N_C}{N_{\mathrm{ANC}}+N_{\mathrm{BNC}}+N_C}.Math.100\%& \mathrm{Equation}4\end{array}$

where N.sub.C, N.sub.ANC, N.sub.BNC are the number of terms in P.sub.C, P.sub.ANC, P.sub.BNC, respectively. SI increases from 0% to 100% when the composition of identical terms increases in two polynomials. The use of Eq. 2 in the search for polynomial terms (flow diagram 4) creates similar polynomials (mean SI>90) and increases the search speed.

[0062] The inventors analyzed the similarity of polynomials from different muscles without the bias from the DOFs that each muscle crosses. To do that, the inventors introduced a DOF-independent polynomial vector for each muscle's musculotendon length polynomial. The Agnostic polynomial vector v=(v.sub.1, . . . , v.sub.n).sup.T of a polynomial is a nonnegative (v.sub.i?0) unit-vector (?.sub.i.sup.nv.sub.i.sup.2=1) with length equal to the number of possible term power compositions in a full polynomial of power ?=5 and maximum muscle dimensionality d=6: n=18. Each element of the vector corresponds to a specific power combination in an ordered list. If a power combination on place i is present in a muscle length polynomial, then v.sub.i is equal to the modulus of the M coefficient (Eq. 1), otherwise v.sub.i=0. The order of power combinations is: [(1, 1, 1, 1, 1), (1, 1, 1, 1), (1, 1, 1, 2), (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1), (1, 2, 2), (1, 2), (1, 3), (1, 4), (1), (2, 2), (2, 3), (2), (3), (4), (5)]. For example, letting P.sub.L=C.sub.1x.sub.1x.sub.2.sup.2+C.sub.2x.sub.1.sup.2x.sub.2+C.sub.3x.sub.1.sup.3+C.sub.4x.sub.1+C.sub.5x.sub.2+C.sub.6, then its vector would have [v.sub.9=|C.sub.1|+|C.sub.2|;v.sub.12=|C.sub.4|+|C.sub.5|;v.sub.16=|C.sub.3|] and all other elements zero. The structural difference of two polynomials was obtained as the Euclidian distance between their vectors. The structural difference is minimal when power composition of all terms and their absolute coefficients are similar in both polynomials even if they cross different DOFs, and large when their power compositions do not have same terms.

[0063] The inventors calculated the amount of memory required for spline approximation as a size of MATLAB's .mat files that contained single-precision spline parameters saved using -v7.3 flag, which enables compression. The inventors calculated the amount of memory required for polynomials as the size of executable .mexw64 files compiled with Visual Studio 2017 C++ with /O2 optimization. The amount of time required to perform the evaluation was obtained using MATLAB's Profiler. Individual samples for mean and standard deviation of evaluation time were obtained per muscle's dataset during estimation of quality of fit. All computations were performed on a regular personal computer (DELL Precision Workstation T5810 XL with Intel Xeon processor E5-2620 v3 2.4 GHz, 64 GB DDR4 RAM, SK Hynix SH920 512 GB SSD operating under Windows 10).

[0064] The composition of approximating polynomials was analyzed with standard statistical tools to test their validity. The root mean square values were used to evaluate errors in the approximated values relative to the dataset used for fitting and the independent testing dataset. The linear regression was used to test the relationship between the complexity of a muscle's physiological function in the form of the number of DOFs it spans and the complexity of the approximating polynomials.

[0065] The similarity of composition across multiple muscle groups was tested with the dimensionality reduction analyses, i.e., principle component analysis (PCA) and hierarchical clustering. The Euclidian distance between the muscle vectors in the DOF-independent basis (described above) was first analyzed with the average linkage hierarchical clustering implemented in SciPy. It is a common approach where the distance from a cluster to another cluster is an average distance between elements of these two clusters. Then, the dominant relationship in this distribution of muscle vectors was analyzed with PCA (Scikit-learn module).

[0066] The representation of structural and functional information within the polynomial structure was further tested by comparing the distributions of the distances between muscles with similar and different structure or function. The normality of these distributions was tested with D'Agostino's K-squared test that measures deviation from normal skewness and kurtosis. For normal distributions, a one-tailed t-test was used to test if distances between similar (functionally or structurally) muscles was smaller than distances between dissimilar muscles. The non-normal distributions were compared with Mann-Whitney U test (from SciPy module), which calculates the likelihood that a sample from one distribution will be less than a sample from another distribution. This test is nearly as efficient as t-test on normal distributions. Additionally, a simpler one-sample test was performed to compare the differences between elements in the two distributions to zero. A sign test was used to test if the median of that distribution was below zero. The sign test was used instead of the Wilcoxon signed-rank test, because the latter assumes symmetrical distribution of differences around the median.

Results

Approximation of Muscle Lengths and Moment Arms

[0067] FIGS. 6A and 6B illustrate histograms 51 and 52 of the normalized error in estimation of muscle lengths and moment arms, respectively, using splines and optimized polynomials with and without the aforementioned constraint associated with steps 21-23 of FIG. 4. For the purposes of error visualization, 1% of outliers (see Table 1) are omitted. In this study, musculoskeletal kinematics of a human hand were precisely (error <3%, see Table 3 below) and efficiently (see Table 4 below) represented as a system of polynomials. FIG. 7A illustrates a graph 55 of similarity index (SI) vs. number of muscles for polynomials defined with the constraint stated as the equality between muscle length partial differentials in local coordinates and its moment arms. It demonstrates that the methods described in FIG. 3 and FIG. 4 produce the muscle length polynomials of similar structure. FIG. 7B illustrates a graph 56 of the number of joints the muscle spans vs. the number of terms in the approximating polynomials, which demonstrates that the number of terms increases with the number of joints the muscle spans. FIG. 7B shows the relationship between the number of terms in the muscle length polynomial (circles) and the number of DOFs each muscle spans (dashed, y=7.3112x?1.5604, r=0.7137, p<3.Math.10.sup.?6). The right side of FIG. 7B shows the distribution of polynomial complexity expressed as the number of terms.

[0068] FIGS. 8A and 8B demonstrate the non-random structure in the composition of polynomials. FIG. 8A shows an average-linkage dendrogram and heatmap of distances between DOF-independent vectors of muscles' lengths. FIG. 8B shows the muscle vectors in the axes of two first principal components corresponding to terms x (horizontal axis) and x.sup.2 (vertical axis).

[0069] A combination of fitting and testing of the dataset was used to evaluate the precision of the known spline model and the polynomial model in accordance with the inventive principles and concepts. Splines and both types of polynomials (adhering and not adhering to the constraint described by Eq. 2) approximate moment arms with <3% error and muscle length with <0.2% error, as can be seen from FIGS. 6A and 6B and Table 3 below. Although the spline approximation error has a smaller deviation from zero, it is much harder to interpret (see Total number of parameters in Table 3). The AIC was used to assess the relative quality of statistical models to represent the phenomena by calculating the tradeoff between increasing precision and adding more variables. The AIC of the polynomial model of the kinematic variables (?1.6*10.sup.7 and ?10.sup.7) is significantly smaller than AIC of the spline model (2.2*10.sup.9 and 3.2*10.sup.10), which shows better relative quality of the polynomial model. Addition of the partial differential constraint (Eq. 2) did not significantly change the precision of the polynomial model (p>0.95 and Table 3) and AIC. Their error distributions in FIGS. 6A and 6B are not distinguishable.

TABLE-US-00003 TABLE 3 The comparison of spline and two polynomial approximations with (constrained) and without (unconstrained) the constraint linking muscle lengths and moment arms, as described by algorithm in Model Physical Constraints in Methods. Values are given ? standard deviation and maximum absolute percent. Approximation used methods used: CS-cubic splines, UP-unconstrained polynomials, CP-constrained polynomials. Normalized Normalized error Total number error, % w/o outliers, % of parameters AIC, au Method L MA L MA L MA L MA CS ?1*10.sup.?4 ? ?0.018 ? ?1*10.sup.?4 ? ?0.018 ? 1.1*10.sup.9 16.4*10.sup.9 2.2*10.sup.9 3.2*10.sup.10 1.2*10.sup.?2, 0.27, 19.46 5.8*10.sup.?3, 0.06 0.22, 1.85 1.23 UP ?2*10.sup.?4 ? ?0.024 ? ?1*10.sup.?4 ? ?0.025 ? 644 749 ?1.6*10.sup.7 ?1.0*10.sup.7 5.2*10.sup.?2, 0.65, 18.68 3.0*10.sup.?2, 0.14 0.54, 2.52 2.5 CP ?2*10.sup.?4 ? ?0.024 ? ?1*10.sup.?4 ? ?0.025 ? 700 841 ?1.6*10.sup.7 ?1.0*10.sup.7 5.2*10.sup.?2, 0.65, 17.77 3.0*10.sup.?2, 0.14 0.54, 2.52 2.4

TABLE-US-00004 TABLE 4 Time and memory requirements of approximations methods for kinematic variables. Time of Time of evaluation, generation, Method ms min Memory, KB CS 128.6633 ? 6.0872 33 17,800,000 UP 0.0147 ? 0.0017 297 139 CP 0.0161 ? 0.0030 114 166

[0070] The distribution of evaluation time for splines and polynomial models was obtained by separating the dataset into 30 muscle-based groups and measuring time spent evaluating the approximation function in each of the groups. Both polynomial models generated with and without Eq. 2 (constrained and unconstrained) are evaluated faster than the spline approximation models (over 10.sup.4 times faster, Table 4) and require less memory (10.sup.5 times smaller). When the relationship between muscle length and moment arm associated with Eq. 2 contributed to the selection of polynomial terms, as described above with reference to FIG. 4, the search time for the best-fit polynomial model decreased by a factor of at least two. This was accomplished without a change in the overall accuracy of fits, as demonstrated by FIGS. 6A and 6B.

Structure of Approximating Polynomials

[0071] Both polynomial models are similar in composition. We examined the difference in polynomial structure, i.e., the presence or absence of terms in functions for muscle lengths, calculated with and without adherence to the length-moment arm constraint (Eq. 1) for the same muscle. With reference again to FIG. 5, it shows that both optimizations found very close polynomials (SI?80%) for a majority of muscles (29). On average, they have a 90% difference, and the maximum difference is about 35%. The differences in structures appear when the constrained polynomials retain the terms adopted from moment arm polynomials.

[0072] The number of polynomial terms in the muscle length grows with the number of degrees of freedom that a muscle crosses (FIG. 7B, r=0.71). However, the relative complexity of the polynomial measured in the fraction of parameter space occupied decreases. Interestingly, thumb muscles (ADPT, FPB, APB, EPB, APL, FPL, EPL) stay above the regression line, indicating a higher than average complexity, while finger muscles (FDS2-5, FDP2-5, ED2-5, EDM, EIND) stay below, suggesting a lower relative complexity.

Structure and Function

[0073] To investigate the information embedded within the polynomials of all muscles, the inventors developed DOF-independent vectors that represented the relative contribution of terms with specific power composition to the overall profile of muscle length polynomial. These nonnegative unit-vectors belong to a space where each axis corresponds to a power composition of a polynomial term with maximum total power of 5 (e.g. x.sub.i.sup.2x.sub.j has power composition (2, 1)). Differences between muscles were then measured as Euclidean distances between their vectors. To visualize the resulting 18-dimensional space, the inventors generated a heatmap with a dendrogram (FIG. 8A) and projected these vectors on two first principle components (FIG. 8B).

[0074] It can be noted in FIGS. 8A and 8B that thumb muscles (ADPT, APB, OP, APL, and EPL, EPB, and FPB to lesser extent) are visibly separated from all other muscles. At the small relative distances, three clusters on the dendrogram and heatmap are visible. They can be assigned a function based on the majority of muscles within them: finger muscles (FDP2-5, FDS4, FDSS, ED2, ED4, EDS, EIND), wrist flexors and rotators located on the forearm (FCU, FCR, PT, PQ, SUP), biceps brachii and extensors (BIC_SH, BIC_LO, ECR_LO, ECR_BR, ECU). A large portion of the muscle vector variance (88%) is explained by the first two principle components. They have their largest coefficients associated with linear (k.sub.12=?0.72) and square (k.sub.15=0.83) power compositions, respectively (index 12 corresponds to axis associated with power combination (1) in the DOF-independent power vector, and 15(2), see Methods). From that, the group of muscles in the bottom-left corner of FIG. 6B is dominated by linear terms, thumb muscles (bottom and bottom-right) rely on linear terms less than others, and brachioradialis (BRD) uses square term much more than the linear (v.sub.12=0.18, v.sub.15=0.95). Overall, the space of the muscle polynomial vectors appears to be not random and suggests internal organization based on muscle anatomy or function.

[0075] FIG. 9A is a graph 61 showing distributions 71 and 72 of distances between muscles that share an anatomical DOF (71) and between muscles that do not share a DOF (72). FIG. 9B is a graph 62 showing a probability density distribution 73 of difference in distance between muscles that share a DOF and muscles that do not. FIG. 9C is a graph 63 showing distributions 74 and 75 of distances between muscles that belong to the same functional group and share a DOF (74) and muscles that do not (75) but share a DOF. FIG. 9D is a graph 64 showing a probability density distribution 76 of difference in distance between muscles that belong to the same functional cluster and muscles that do not, while all of them share a DOF. Box plots in FIGS. 9A, 9B, 9C and 9D indicate a median and 25.sup.th-75.sup.th quantile region. Asterisks in FIGS. 9A, 9B, 9C and 9D indicate p<10.sup.?8 in the statistical comparisons with ?=0.05.

[0076] To determine whether the muscle vectors contain information about their anatomical structure, the inventors performed attest to determine whether muscles crossing the same DOFs will be closer to each other in the vector space than to muscles that do not cross the DOF. To do that, the inventors generated three distributions: distances between muscles that share a DOF (FIG. 9A, bars 71); distances between muscles that do not share a DOF (FIG. 9A, bars 72); difference in distance (FIG. 9B, bars 73). The first distribution (FIG. 9A, bars 71) contains distances between two muscles, both crossing the DOF, for all DOFs. The second distribution (bars 72) contains distances between two muscles, one of which crosses the DOF, and the other of which does not, for all DOFs. In this approach, the distance between two muscles may appear in the first distribution 71 when looking at one DOF, and the second distribution 72 when looking at another DOF. The third distribution (FIG. 9B, bars 73) contains all possible differences in distance between muscles: DD=d(A, B)?d(A, C), where muscles A and B share a DOF, A and C do not, with respect to each DOF. Because of similarity between finger joints (MCP, PIP, DIP) of different fingers in our model and lack of hand-based finger muscles, MCP of fingers 2-5 were treated as equal in this analysis, as were PIP and DIP.

[0077] All three distributions 71-73 were not normal (D'Agostino, p<10.sup.?8). The first two distributions 71 and 72 were significantly different with muscles that have similar anatomical paths being closer to each other (Mann-Whitney U=8.Math.10.sup.5, p<10.sup.?8). The median of the third distribution 73 was less than zero (sign test, p<10.sup.?8). These results support that DOF-independent muscle vectors contain information on muscle anatomy. FIGS. 9A and 9B demonstrate that the polynomial term composition of the muscle length polynomials captures the anatomical relationship among muscles. FIGS. 9C and 9D demonstrate that the polynomial term composition of the muscle length polynomials captures the functional relationship among muscles.

[0078] To determine whether the muscle vectors contain information about their physiological function, not explained by the anatomical similarities, the inventors performed tests to determine whether muscles that share a DOF, but have different functions, will be farther apart than muscles that share a DOF and have similar function. Again, three distributions 74-76 were generated: distances between muscles that share a DOF and are within the same functional group (FIG. 9C, bars 74); distances between the muscles that share a DOF but belong to different functional groups (FIG. 9C, bars 75); difference in distance (FIG. 9D, bars 76). All modelled muscles were separated into seven functional groups: wrist supinators (BIC_LO, BIC_SH, BRD, SUP), pronators (PT, PQ), extensors (ECR_LO, ECR_BR, ECU), flexors (FCR, FCU, PL), finger flexors (FDS2-5, FDP2-5), extensors (ED2-5, EDM, EIND), and thumb muscles (APL, OP, APB, EPL, EPB, FPB, FPL, ADPT). Each muscle was assigned to a group based on its primary function in the hand and forearm.

[0079] All three distributions 74-76 were again not normal (D'Agostino, p<10.sup.?8). The distributions 74 and 75 were significantly different with muscles that have similar function being closer to each other (Mann-Whitney U=5.Math.10.sup.6, p<10.sup.?8). The median of the third distribution 76 was less than zero (sign test, p<10.sup.?8). These results support the conclusion that DOF-independent muscle vectors contain information on muscle function not explained by the muscle anatomy.

[0080] Although both tests showed significance, the median in FIG. 9B is almost twice as far from zero as the median in FIG. 9D (?0.13 and ?0.07, respectively). In summary, these results support the idea that the polynomial term composition of muscle lengths is not random and reflects muscle anatomy and function.

[0081] FIG. 10 is a block diagram showing the system 100 in accordance with a representative embodiment that enables biomimetic processing of biological inputs in order to generate control signals for controlling a myoelectric prosthetic device in real-time. A biomimetic controller 101 of the system comprises a signal processor 102, musculoskeletal model 103 and a polynomial (Poly) block 104. The signal processor 102 receives M biological signals from a subject, where M is a positive integer that is greater than or equal to 1, and expands the M biological signals into N activation signals, where N is a positive integer that is greater than M. The activation signals are outputted from the signal processor 102 and are inputted to the musculoskeletal model 103. The musculoskeletal model 103 converts the activation signals into intended motion signals, which are outputted from the musculoskeletal model 103 and inputted to a prosthesis controller 105 of the system 100.

[0082] The prosthesis controller 105 converts the intended motion signals into control signals, which are outputted from the prosthesis controller 105 and inputted to a prosthesis device 106 that is worn by a subject, or patient (not shown). The prosthesis device 106 performs one or more tasks in accordance with the control signals received from the prosthesis controller 105.

[0083] In accordance with an embodiment, the prosthesis device 106 comprises one or more sensors that detect motion of the prosthesis device 106 as it performs one or more tasks in accordance with the control signals received from the prosthesis controller 105. The output of the sensor(s) is fed back to the Poly block 104. The Poly block 104 uses this feedback in approximating the muscle dynamics in accordance with the approximation method of the parent application described above with reference to FIGS. 1-9B. As indicated above, the polynomial structures of the Poly block 104 preferably are determined a priori to allow the system 100 to operate in real-time. The computation-intensive simulation of musculotendon kinematics is replaced by accurate and optimal approximations of this process. The approximated muscle dynamics are inputted to the musculoskeletal model 103, which uses them in generating the intended motion signals that are delivered to the prosthesis controller 105. This allows the prosthesis controller 105 to modify, if necessary, the control signals that are delivered to the prosthesis device 106 to better control the tasks that are being performed by the prosthesis device.

[0084] In accordance with another embodiment, the system 100 includes one or more instrumented objects 107 that the prosthesis device 106 interacts with while performing tasks. The instrumented object(s) 107 output feedback signals that reflect the motion of the instrumented object(s) and/or interaction (e.g., gripping, picking up) between the prosthesis device 105 and the instrumented object(s) 107. These feedback signals may be used by the signal processor 101 to expand the M biological signals into the N activation signals.

[0085] Biological signals can be grouped into agonists and antagonists based on their anatomy. This relationship can be represented mathematically to expand sparse biological signals into higher-dimensional activation signals. The activation signals produce movements through mechanical coupling, which defines the space of independent DOFs that are possible given the particular set of sparse biological signals. FIG. 11 illustrates a dendrogram that shows the association of sparse input signals with the full set of simulated signals inside the signal processor 102 and lists acronyms corresponding to a set of N simulated activation signals that are generated from a subset of M available biological signals based on the illustrated dendrogram. For example, if only four (M=4) biological signals from wrist and finger muscles are available (e.g., FCU, ECU, FDS2, and ED3), then activation signals will be produced at the cluster level 5. Each biological signal is copied to other members of its cluster and scaled with a coefficient that is proportional to the anatomical relationship between each activation signal and the source biological signal.

[0086] Thus, in the system 100, the number of available biological signals is smaller than the number of activation signals and is smaller than the number of DOFs that are controlled by the prosthesis controller 105. In accordance with a representative embodiment, the system 100 is capable of simultaneously controlling at least three DOFs, and typically at least four DOFs, with a loop time that can be less than 2 milliseconds (ms), which is not believed to have been possible until the present invention. The loop time is defined as the time between the moment of sending a packet of biological signals to the system 100 and the moment of a set of output control signals from the controller 105, at which point the system is ready to process the next packet of biological signals.

[0087] Although it will be understood that the inventive principles and concepts presented herein are not limited to any particular anatomical feature, examples of DOFs, as that term is used herein, include: [0088] 1 DOF is flexion/extension of 2nd-5th metacarpophalangeal joints driven by a single control signal (all fingers 2-5 move together); [0089] 1 DOF is flexion/extension of 1st carpometacarpal joint of the thumb driven by a single control signal (independent control of the thumb); [0090] 1 DOF is abduction/adduction of 1st carpometacarpal joint of the thumb driven by a single control signal (independent control of the thumb); and [0091] 1 DOF is flexion/extension of wrist joint driven by a single control signal (independent control of the wrist).

[0092] FIG. 12 is a block diagram showing the system 120 in accordance with a representative embodiment that enables biomimetic processing of biological inputs in order to generate control signals for controlling a virtual reality (VR) prosthesis system. The signal processor 102 receives M biological signals from a subject, where M is a positive integer that is greater than or equal to 1, and expands the M biological signals into N activation signals, where N is a positive integer that is greater than M. The activation signals are outputted from the signal processor 102 and are inputted to the musculoskeletal model 103. The musculoskeletal model 103 converts the activation signals into intended motion signals, which are outputted from the musculoskeletal model 103 and inputted to the prosthesis controller 105 of the system 120.

[0093] The prosthesis controller 105 converts the intended motion signals into control signals, which are outputted from the prosthesis controller 105 and inputted to the VR prosthesis system 108 that is worn by a subject or patient (not shown). The VR prosthesis system 108 moves the avatar of the prosthesis or the user's hand in accordance with the control signals received from the prosthesis controller 105. Direct control of four or more DOFs of the avatar can mean, but is not limited to, virtual gripper opening and closing with simultaneous flexion or extension and rotation of the wrist and flexion or extension or the elbow.

[0094] In accordance with this embodiment, the VR prosthesis system 108 measures virtual motions it performs or virtual interactions it performs with one or more objects in accordance with the control signals received from the prosthesis controller 105 and outputs feedback signals that reflect the virtual motions and/or virtual interactions. These feedback signals may be used by the signal processor 101 when it performs the algorithm described above that expands the M biological signals into the N activation signals.

[0095] In addition, the intended motion signals are fed back to the Poly block 104 and processed by the Poly block 104 to approximate the muscle dynamics that are delivered to the musculoskeletal model 103. The musculoskeletal model 103 processes the activation signals and the approximated muscle dynamics to generate the intended motion signals, which are then processed by the prosthesis controller 105 to generate the control signals that are delivered to the VR system 108.

[0096] The feedback signals and the manner in which they are processed in the system 120 allow the control signals that are delivered to the VR system 108 to be varied to achieve more precise control of the VR system 108. This, in turn, allows the VR system 108 to be used for training.

[0097] Despite technological advances in prosthetic design, myoelectric prostheses can be difficult to control. The forethought required to operate this type of device in a complex way can be quite burdensome. This can lead to passive-use of the device, which can have detrimental effects on the contralateral limb due to overuse. Moreover, several studies suggest an increased rate of rejection of myoelectric prostheses with lengthened follow-up. Providing extensive training as well as intuitive and robust control for myoelectric prostheses may reduce injuries and increase usability.

[0098] In an experimental setup of the system 120 shown in FIG. 12, the VR environment of the VR system 108 includes a dynamic model of a prosthetic hand and simulated its interaction with the external world, providing the user with visual feedback. This type of environment allows the patient to learn how to use a prosthetic device and to select a prosthetic device that is most suitable for the patient. Once a patient is fitted with a prosthetic device, its success is based on its usefulness in everyday life. Thus, the ability to enable a patient to train on the system 120 before selecting and being fitted with a prosthetic limb is very beneficial. In addition, studies have been conducted that show that virtual reality enables the brain to embody a virtual limb and thus help reduce phantom pain. Other studies show that a technique that involves virtual reality and neural stimulation can help change an amputee's phantom limb to more closely match their prosthetic limb, making it easier and more natural to use.

[0099] The system 120 can function as a tool to improve fitting, adjustment, and usability of high DOF prostheses. The system 120 can encompass all phases of interactions between health professionals and patients, including preliminary prosthesis selection using virtual reality at home, clinic-based fitting and assessment of patient performance with the prosthesis, and clinic- and home-based rehabilitation. The clinicians can tune the prosthesis controller 105 to the patient's needs and to the level of amputation, which determines the number of available biological signals and, consequently, the number of available functions. Patients would be more involved in the prosthesis selection process through testing and familiarization with multiple devices and controller settings. Through better understanding of the needs and limitations of the user at the beginning of the process, clinicians can more efficiently fit complex prosthetics and provide customized training.

[0100] FIG. 13 is a block diagram of the system 130 in accordance with an embodiment that combines the features of the systems 100 and 120 shown in FIGS. 10 and 12, respectively, to enable biomimetic processing of biological inputs in order to generate control signals for controlling the VR prosthesis system 108 or the prosthesis device 106. In accordance with this representative embodiment, the system 130 includes a switching device 131 comprising first and second switching elements 131a and 131b, respectively. In a first switching configuration of the switching device 131, the first switching element 131a interconnects the prosthesis controller 105 with the VR system 108 and the second switching element 131b interconnects the musculoskeletal model 103 with the Poly block 104. This causes the system 130 to operate in the manner described above with reference to FIG. 12. In a second switching configuration of the switching device 131, the first switching element 131a interconnects the prosthesis controller 105 with the prosthesis device 106 and the second switching element 131b interconnects the prosthesis device 106 with the Poly block 104. This causes the system 130 to operate in the manner described above with reference to FIG. 10.

[0101] FIG. 14 is a flow diagram depicting the method in accordance with a representative embodiment. With reference to block 141, a signal processor of a mimetic controller, a signal processing algorithm is performed that processes M biological signals received from a residual limb at an input port of the signal processor to transform the M biological signals into N activation signals, where M and N are integers and M is less than N, the N activation signals being outputted from the output port. With reference to block 142, a musculoskeletal model of the mimetic controller performs a modeling algorithm that transforms the N activation signals received at an input port of the musculoskeletal model into intended motion signals and outputs the intended motion signals from an output port of the musculoskeletal model. With reference to block 143, a prosthesis controller of the system performs a control algorithm that transforms the intended motion signals received at an input port of the prosthesis controller into control signals that are outputted from an output port of the prosthesis controller. With reference to block 144, a controlled device receives the control signals and moves four or more DOFs simultaneously in accordance with the control signals. Direct control of four or more DOFs can mean, but is not limited to, hand opening and closing in a power grip with simultaneous flexion or extension of the wrist end rotation of the wrist.

[0102] It should be noted that although the inventive principles and concepts disclosed herein have been described with reference the prosthesis controller 105 controlling a prosthesis device 106 (e.g., a prosthetic limb) or a VR prosthesis system 108, the controlled device may be other types of devices such as, for example, active assistive devices (e.g. exoskeletons, muscle stimulation systems, etc.), computer interface devices (e.g., game controllers, gesture-based interactive systems, etc.), and other peripherals (e.g., drones, robotic devices, etc.).

[0103] As indicated above, the four or more control signals cause the controlled device to move that many or fewer DOFs of the prosthesis or other device under the direct and simultaneous control of the biological signals. For example, the control signals can cause the controlled device to perform one or more tasks with at least four DOFs with a loop time that is less than 2 ms.

[0104] FIG. 15 is a flow diagram of modifications to the method represented by the flow diagram of FIG. 14 for the case where the controlled device referred to in step 144 is a VR prosthesis system or a prosthetic limb. With a switching device of the system, placing the VR prosthesis system and the prosthetic limb in communication with the prosthesis controller when the switching device is in first and second switching configurations, respectively, as indicated by block 151. With the switching device in the first switching configuration, the VR prosthesis system receives the control signals from the prosthesis controller and performs one or more tasks in accordance with the control signals, as indicated by block 152. With the switching device is in the second switching configuration, the prosthetic limb receives the control signals from the prosthesis controller and performs one or more tasks in accordance with the control signals, as indicated by block 153.

[0105] FIG. 16 is a flow diagram in accordance with a representative embodiment in which the method represented by the flow diagram of FIG. 15 further comprises the following. First and second sets of feedback signals are output from the VR prosthesis system and the prosthetic limb, respectively, when the switching device is in the first and second switching configurations, respectively, as indicated by block 161. Each of the first and second sets of feedback signals describes a virtual motion within the VR prosthesis system and an actual motion of the prosthetic limb, respectively. With reference to block 162, the first and second sets of feedback signals are fed back to the signal processor when the switching device is in the first and second switching configurations, respectively. With reference to block 163, the first and second sets of feedback signals are used by the signal processor to transform the M biological signals into the N activation signals.

[0106] FIG. 17 is a flow diagram in accordance with a representative embodiment in which the method represented by the flow diagram of FIG. 16 further comprises the following. With reference to block 171, third and fourth sets of feedback signals are output from the musculoskeletal model and the prosthetic limb, respectively. With a Poly block of the mimetic controller, when the switching device is in the first switching configuration, the third set of feedback signals is received and used by the Poly block to approximate muscle dynamics that are outputted to the musculoskeletal model, as indicated by block 172. With reference to block 173, the approximated muscle dynamics are used by the musculoskeletal model to generate the intended motion signals. With reference to block 174, when the switching device is in the second switching configuration, the fourth set of feedback signals is received in the Poly block from the prosthetic limb and used by the Poly block to approximate muscle dynamics that are outputted to the musculoskeletal model. With reference to block 175, the muscle dynamics are used by the musculoskeletal model to generate the intended motion signals.

[0107] The methods described above are typically implemented in software, firmware, or a combination thereof, executed on one or more processors, controllers or computers. Alternatively, the methods may be implemented solely in hardware, such as a state machine or an application specific integrated circuit (ASIC), for example. The software, firmware, or combination thereof, is stored in one or more memory devices that may be part of the biomimetic controller 101 or the prosthesis controller 105, depending on which part of the method is being performed.

[0108] FIGS. 18A-18C are graphs demonstrating multi-dimensional control of a controlled device, e.g., a prosthetic limb, by the systems shown in FIGS. 10, 12 and 13 in accordance with a representative embodiment. FIG. 18A shows an example of experimental and simulated temporal profiles 181 and 182, respectively, of a hand movement, where the wrist was flexed then extended through the whole range of motion without pronating or supinating (i.e., neutral pronation and supination (pro-sup)) and with fingers extended. These movements involved 18 DOF of the hand. EMG-driven real-time simulations reproduced the recorded experimental motion very closely. FIGS. 18B and 18C demonstrate the performance across multiple hand movements, such as palm up and down, wrist flex and extend, fingers flex and extend, and similar movements. The angular root mean squared (RMS) error between simulated and recorded motions was very low for both moving joints (FIG. 18B) and static joints that were not moving but had to be held still with active forces (FIG. 18C).

[0109] It should be emphasized that the above-described embodiments of the present invention, particularly, any preferred embodiments, are merely possible examples of implementations, merely set forth for a clear understanding of the principles of the invention. Many variations and modifications may be made to the above-described embodiment(s) of the invention without departing substantially from the spirit and principles of the invention. All such modifications and variations are intended to be included herein within the scope of this disclosure.

[0110] For example, while the inventive principles and concepts have been described herein with reference to controlling a prosthetic 50, the described software and/or firmware can be used in other applications that require fast and memory-efficient approximation of complex multidimensional data, such as, for example, with robots or autonomous drones controlled by small chips that need to approximate information about interactions with objects or terrain, that are originally calculated using systems of differential equations.