Exoskeleton

Abstract

An exoskeleton for humans including a joint element that interacts directly or indirectly with a human's joint via an end-effector mount, wherein the end-effector mount is arranged to perform an arbitrary planar parallel movement in a plane, allowing superimposed translational and rotational movements of the end-effector mount relative to a body of the joint element. The exoskeleton allows for excellent adjustment of the joint axes, i.e. the exoskelleton's and the human's joint, for effecting simultaneous translational and rotational movements. Particularly, the exoskeleton is self-aligning to the movements of a human's joint independent from differences in the attachment of the exoskeleton to the body and anatomical differences of the patients.

Claims

1. A powered exoskeleton configured to actively move a joint of a human, the exoskeleton comprising: a) a joint element configured to interact with a human's joint via an end-effector mount configured to be directly connectable to the human's joint, wherein b) the end-effector mount is arranged to perform an arbitrary planar parallel movement in a plane, allowing superimposed translational and rotational movements of the end-effector mount relative to a body of the joint element, wherein c) the joint element is configured to be actively driven by at last one back-drivable actuator for actively moving the human's joint; and d) the joint element is configured to be passively driven by the human for self-alignment of the exoskeleton to the human's joint.

2. The exoskeleton according to claim 1 wherein the joint element comprises a parallel mechanism.

3. The exoskeleton according to claim 1, wherein the end-effector mount comprises at least three translational axes, wherein the axes a) are rigidly connected to the end-effector mount; b) are arranged in parallel to the plane of the arbitrary planar parallel movement of the end effector; and c) are arranged having an angle to each other.

4. The exoskeleton according to claim 3, wherein the end effector mount comprises three translational axes and the angle between two axes is 100-140.

5. The exoskeleton according to claim 1, wherein axes are respectively guided by linear bearings, wherein the linear bearings are configured to be independently movable on one or more circular paths relative to the body, wherein the one or more circular paths are arranged in parallel to the plane of the arbitrary planar parallel movement of the end-effector mount.

6. The exoskeleton according to claim 5, wherein the linear bearings are movable along one common circular path.

7. The exoskeleton according to claim 5, wherein the linear bearings are respectively supported by rotational bearings with respect to the one or more circular paths, wherein the rotation axes of the rotational bearings are arranged perpendicular to the plane of the arbitrary planar parallel movement of the end-effector mount.

8. The exoskeleton according to claim 7, wherein the rotational bearings are connected to co-centered rings.

9. The exoskeleton according to claim 8, wherein one or more or all of the linear bearings are actively independently driven along the one or more circular paths by respective motors that drive said co-centered rings.

10. The exoskeleton according to claim 8, wherein one or more or all of the linear bearings are actively independently driven along the one or more circular path by cable based actuators that drive said co-centered rings.

11. The exoskeleton according to claim 5, wherein the axes comprise straight links that are supported in corresponding openings of the linear bearings.

12. The exoskeleton according to claim 5, wherein the joint element is configured to be passively driven by arranging the end-effector mount so that one or more or all of the linear bearings are configured to be driven by the movements of the human's joint within the plane of the planar parallel movement.

13. The exoskeleton according to claim 5, wherein one or more or all of the linear bearings are resisted with springs or brakes.

14. The exoskeleton according to claim 5, wherein one or more linear bearings are actively independently driven and the remaining linear bearings are resisted with springs or brakes.

15. The exoskeleton according to claim 1, further comprising measuring devices for measuring or registering a motion of the human's joint, a force of the human's joint, or a relationship between the motion of the human's joint and the force of the human's joint.

16. The exoskeleton according to claim 1, wherein the exoskeleton is configured to actively move a knee, shoulder, elbow, pelvis, ankle or spine joint.

17. A method for using an exoskeleton of claim 1, the method comprising using the exoskeleton of claim 1 for executing the following steps: a) actively moving a human's joint; and/or b) measuring a human's joint motion; and/or c) measuring a human's exerted joint force; d) measuring the relationship between a human's joint motion and a human's joint force and/or e) passively applying resistance to movements of a human's joint.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) In the following preferred embodiments of the invention are disclosed with reference to the figures:

(2) FIG. 1 depicts shoulder and elbow movements.

(3) FIG. 2 illustrates the scapulohumeral rhythm at the shoulder

(4) FIGS. 3A and 3B illustrate the conceptual design of an embodiment of a exoskeleton according to the invention, used as a shoulder-elbow exoskeleton.

(5) FIGS. 4A and 4B are a schematic representation of anterior-posterior translation during flexion/extension movement of the knee joint.

(6) FIG. 5 shows a part of an embodiment of the exoskeleton according to the invention attached to a human knee.

(7) FIG. 6 shows an embodiment of a joint element of the exoskeleton of FIG. 5 illustrating the axes and angles used.

(8) FIG. 7A shows the embodiment of the joint element of FIG. 6 in a top view.

(9) FIG. 7B shows the embodiment of the joint element of FIG. 6 in a side view. The embodiment uses three co-centered rings that are driven internally using a belt drive transmission. The rings are supported and aligned using custom brackets manufactured from aluminum and teflon ball rollers.

(10) FIG. 8 shows another embodiment of a joint element of an exoskeleton according to the invention with built in force/torque sensing. Three load cells and a torque cell are attached to the end effector to measure forces/torques applied.

(11) FIG. 9 shows another embodiment of a joint element of an exoskeleton according to the invention having series-elastic actuation of the self-aligning joint element. Deflections of a compliant mechanism attached to the end effector mount are measured to estimate forces/torques applied.

(12) FIG. 10 shows another embodiment of a joint element of an exoskeleton according to the invention having a variable-impedance antagonist actuation of the self-aligning joint element via cable actuators.

(13) FIG. 11 is a block diagram of an impedance control architecture.

(14) FIG. 12 illustrates a position tracking performance of a controller as tested using a typical trajectory for the knee joint. The path used to test position tracking performance is a rough visualization of tibial translation of the knee joint. In the desired path, the center of knee joint translates up to 15 mm during a 90 knee extension.

(15) FIG. 13 shows schematic representations of six different parallel mechanisms that can be used as joint element of an embodiment of the exoskeleton according to the invention.

(16) FIG. 14 shows a three-dimensional view including a detailed frontal view D of a joint element that is driven by cable based actuators.

DESCRIPTION OF PREFERRED EMBODIMENTS

(17) In the following preferred embodiments of an exoskeleton for humans is described with reference to the figures. Features of one embodiment can be used in other embodiments, too, if applicable.

(18) The exoskeleton 1 can be used at many human joints, including but not limited to knee, shoulder, hip/pelvis, ankle, and spine.

(19) a. Design of the 3-DoF Self-Aligning Joint Element

(20) In general a parallel mechanism, as illustrated in FIG. 13 in six variations, can be used as underlying mechanism for implementing a joint element 2 for an exoskeleton 1 according to the invention. The use of such a kinematics in an exoskeleton 1 for rehabilitation, human augmentation, human measurement and many other purposes ensures ergonomy, large range of motion for joint movements, the ability to deliver and measure joint translations together with joint rotations, allows an ease of attachment due to no calibration requirements and many other advantages. It should be noted that the exoskeleton can of course also be used for animals.

(21) A 3-RRP mechanism is preferred as the underlying mechanism for implementation of self-aligning joint element, since this mechanism is capable of sustaining all necessary movements to cover the complex movement of the joints whose axis of rotation are not fixed. In particular, the 3-RRP planar parallel mechanism possesses 3 DoF, which include translations in plane and rotation along perpendicular axis. Thanks to its kinematic structure with close kinematic chains, the 3-RRP mechanism features high bandwidth and position accuracy when compared with its serial counterparts. Moreover, the workspace of 3-RRP mechanism covers a large range of rotations, which is necessary for implementation of the shoulder joint whose rotation typically exceeds 180 during flexion and extension exercises. 3-RRP means that the mechanism comprises 3 joints, wherein each of the three joints allows rotation around two different rotational axes and allows displacement along one prismatic axis. The underlining indicates that one rotational axis is actuated. In the example shown in FIGS. 6, 7A and 7B the 3-RRP mechanism comprises three axes 16, 26, 36 that are respectively guided by three joints (bearings 10, 20, 30) which respectively rotate around a vertical axis through point O causing circular paths 14, 24, 34 of the bearings 10, 20, 30 (R), additionally rotate around vertical rotational bearings 12, 22, 32 (R) and finally allow a linear displacement (P) of links 17, 27, 37 within the bearings 10, 20, 30. The links 17, 27, 37 are collinear with the respective axes 16, 26, 36.

(22) As it can be seen in FIG. 6 the 3-RRP mechanism used in the joint element 2 consists of five rigid bodies 3, 18, 28, 38 and a symmetric body 4. Body 3 represents the fixed frame, bodies 18, 28 and 38 have simple rotations about the fixed link about point O, while the symmetric end effector mount 4 is attached to bodies 18, 28 and 38 through linear bearings 10, 20, 30 and rotational bearing 12, 22, 32 collocated at points P, Q and R, respectively. The common out of the plane unit vector is denoted by {right arrow over (k)} and basis vectors of each body are indicated in FIG. 6. In the figure, the point O is fixed in body 3, point P is fixed in body 28, point Q is fixed in body 18, point R is fixed in body 38 and point Z is fixed in end effector mount 4.

(23) Dimensions of the mechanism are defined as follows: The fixed distance OP is defined as I.sub.1, OQ is defined as I.sub.2 and OR is defined as I.sub.3, while the distance ZP is defined as s.sub.1, ZQ is defined as s.sub.2 and ZR is defined as s.sub.3. The angle between the line I and {right arrow over (t.sub.1)} vector is q.sub.1, the angle between I {right arrow over (s.sub.1)} and is q.sub.2 and the angle between I and {right arrow over (v.sub.1)} is q.sub.3. All angles are positive when measured counter clockwise.

(24) For the kinematic analysis, the inputs to the mechanism are set as the angles q.sub.1, q.sub.2 and q.sub.3 (i.e. the links S, T and V are actuated) and their time derivatives. At the initial configuration {right arrow over (e.sub.i)} vector is parallel to {right arrow over (n.sub.1)}. The output of the system is defined as the position of the end-effector mount point Z, when measured from the fixed point O and the orientation of body E, measured with respect to body N. In particular, the scalar variables for outputs are defined as

(25) $x={\stackrel{.fwdarw.}{r}}^{\mathrm{OZ}}.Math.\stackrel{.fwdarw.}{n_1},y={\stackrel{.fwdarw.}{r}}^{\mathrm{OZ}}.Math.\stackrel{.fwdarw.}{n_2},\mathrm{and}=a\tan 2\left(\frac{\stackrel{.fwdarw.}{e_2}.Math.\stackrel{.fwdarw.}{n_2}}{\stackrel{.fwdarw.}{e_2}.Math.\stackrel{.fwdarw.}{n_2}}\right)$ where {right arrow over (r)}OZ is the position vector between points O and Z.
b. Kinematics of the 3-RRP Mechanism

(26) Both forward and inverse kinematics of the exoskeleton are derived at configuration and motion levels, respectively.

(27) 1) Configuration Level Kinematics: To ease calculations, three auxiliary reference frames, namely K, L and M are defined as: {right arrow over (k.sub.1)} extends from Z to P, {right arrow over (l.sub.1)} extends from Z to S and {right arrow over (m.sub.1)} extends from Z to R, while {right arrow over (k.sub.3)}={right arrow over (l.sub.3)}={right arrow over (m.sub.3)}={right arrow over (n.sub.3)}. Using the auxiliary reference frames, the vector loop equations that govern the geometry of the mechanism can be expressed as
x.Math.{right arrow over (n.sub.1)}+y.Math.{right arrow over (n.sub.2)}+s.sub.1.Math.{right arrow over (k.sub.1)}l.sub.1.Math.{right arrow over (t.sub.1)}={right arrow over (0)}(1)
x.Math.{right arrow over (n.sub.1)}+y.Math.{right arrow over (n.sub.2)}+s.sub.2.Math.{right arrow over (l.sub.1)}l.sub.1.Math.{right arrow over (s.sub.1)}={right arrow over (0)}(2)
x.Math.{right arrow over (n.sub.1)}+y.Math.{right arrow over (n.sub.2)}+s.sub.3.Math.{right arrow over (m.sub.1)}l.sub.3.Math.{right arrow over (v.sub.1)}={right arrow over (0)}(3)

(28) Expressing the vector loops in one of the frames (typically in 3), these vector equations yield 6 independent scalar equations, which form the base for solution of configuration level kinematics.

(29) a) Configuration Level Forward Kinematics: Three vector equations that are derived in the previous subsection yield to six nonlinear scalar equations with six unknowns. Given q.sub.1, q.sub.2 and q.sub.3, solving these nonlinear equations analytically for x, y and (and intermediate variables s.sub.1, s.sub.2 and s.sub.3) yields

(30) $\begin{array}{cc}x=-\frac{M}{\sqrt{(}3)\left(K^2+L^2\right)}& \left(4\right)\\ y=c_{22}-\frac{K}{L}{c}_{21}-\frac{\mathrm{KM}}{\sqrt{(}3)L\left(K^2+L^2\right)}& \left(5\right)\\ ={\tan }^{-1}\left(\frac{K}{L}\right)& \left(6\right)\end{array}$ where
K=c.sub.12+c.sub.32+{square root over (3)}c.sub.312c.sub.22{square root over (3)}c.sub.11
L=c.sub.11+c.sub.31+{square root over (3)}c.sub.122c.sub.21{square root over (3)}c.sub.32
M=L(L{square root over (()}(3)K)c.sub.12L(K+{square root over (()}(3)L)c.sub.11
(L{square root over (()}(3)K)Lc.sub.22Kc.sub.21)
c.sub.11=l.sub.1 cos(q.sub.1),c.sub.12=l.sub.1 sin(q.sub.1)
c.sub.21=l.sub.2 cos(q.sub.2),c.sub.22=l.sub.2 sin(q.sub.2)
c.sub.31=l.sub.3 cos(q.sub.3),c.sub.32=l.sub.3 sin(q.sub.3)

(31) b) Configuration Level Inverse Kinematics: Given x, y and e, the inverse kinematics problem can be solved analytically for joint rotations q.sub.1, q.sub.2 and q.sub.3 by using the vector cross product method suggested by Chace (M. A. Chace, Development and application of vector mathematics for kinematic analysis of three-dimensional mechanisms, Ph.D. dissertation, University of Michigan, 1964) as

(32) $\begin{array}{cc}{q}_1={\tan }^{-1}\left(\frac{M_1}{L_1}\right)& \left(7\right)\\ q_2={\tan }^{-1}\left(\frac{M_2}{L_2}\right)& \left(8\right)\\ q_3={\tan }^{-1}\left(\frac{M_3}{L_3}\right)\mathrm{where}{K}_1=x\sin \left(+\frac{}{3}\right)-y\cos \left(+\frac{}{3}\right)K_2=x\sin \left(+\right)-y\cos \left(+\right)K_3=x\sin \left(-\frac{}{3}\right)-y\cos \left(-\frac{}{3}\right)M_1=K_1\cos \left(+\frac{}{3}\right)-\sqrt{(}{l}_1^2-K_1^2)\sin \left(+\frac{}{3}\right)L_1=-K_1\sin \left(+\frac{}{3}\right)-\sqrt{(}{l}_1^2-K_1^2)\cos \left(+\frac{}{3}\right)M_2=K_2\cos \left(+\right)-\sqrt{(}{l}_2^2-K_2^2)\sin \left(+\right)L_2=-K_2\sin \left(+\right)-\sqrt{(}{l}_2^2-K_2^2)\cos \left(+\right)M_3=K_3\cos \left(-\frac{}{3}\right)-\sqrt{(}{l}_3^2-K_3^2)\sin \left(-\frac{}{3}\right)L_3=-K_3\sin \left(-\frac{}{3}\right)-\sqrt{(}{l}_3^2-K_3^2)\cos \left(-\frac{}{3}\right)& \left(9\right)\end{array}$

(33) 2) Motion Level Kinematics: Motion level kinematic equations are derived by taking the time derivative of the vector loop equations derived for configuration level kinematics. Six independent scalar equations can be obtained by projecting the vector equations onto the {right arrow over (n.sub.1)} and {right arrow over (n.sub.2)} unit vectors.

(34) a) Motion Level Forward Kinematics: Given actuator {dot over (q)}.sub.1, {dot over (q)}.sub.2 and {dot over (q)}.sub.3, motion level forward kinematics {dot over (x)}, {dot over (y)} and {dot over ()} problem can be solved for end-effector mount velocities (along with intermediate variables {dot over (s)}.sub.1 {dot over (s)}.sub.2 and {dot over (s)}.sub.3) as
{dot over (X)}.sub.1=A.sub.1.sup.1B.sub.1(10) where

(35) $A_1=\left(\begin{array}{cccccc}1& 0& -s_1\sin \left(+\frac{}{3}\right)& \cos \left(+\frac{}{3}\right)& 0& 0\\ 0& 1& s_1\cos \left(+\frac{}{3}\right)& \sin \left(+\frac{}{3}\right)& 0& 0\\ 1& 0& -s_2\sin \left(+\right)& 0& \cos \left(+\right)& 0\\ 0& 1& s_2\cos \left(+\right)& 0& \sin \left(+\right)& 0\\ 1& 0& -s_3\sin \left(-\frac{}{3}\right)& 0& 0& \cos \left(-\frac{}{3}\right)\\ 0& 1& s_3\cos \left(-\frac{}{3}\right)& 0& 0& \sin \left(-\frac{}{3}\right)\end{array}\right)$${\stackrel{.}{X}}_1=\left(\begin{array}{c}\stackrel{.}{x}\\ \stackrel{.}{y}\\ \stackrel{.}{}\\ {\stackrel{.}{s}}_1\\ {\stackrel{.}{s}}_2\\ {\stackrel{.}{s}}_3\end{array}\right)\mathrm{and}{B}_1=\left(\begin{array}{c}-l_1{\stackrel{.}{q}}_1\sin \left(q_1\right)\\ l_1{\stackrel{.}{q}}_1\cos \left(q_1\right)\\ -l_2{\stackrel{.}{q}}_2\sin \left(q_2\right)\\ l_2{\stackrel{.}{q}}_2\cos \left(q_2\right)\\ -l_3{\stackrel{.}{q}}_3\sin \left(q_3\right)\\ l_3{\stackrel{.}{q}}_3\cos \left(q_3\right)\end{array}\right)$

(36) b) Motion Level Inverse Kinematics: Given the solution of motion level forward kinematics, the motion level inverse kinematics problem can be solved by trivial application of linear algebra; hence, the solution is omitted from discussion due to space considerations.

(37) c. Embodiment of the Self-Aligning Joint Element

(38) FIG. 7 shows a self-aligning joint element 2 of the exoskeleton 1 based on the 3-RRP mechanism that can be applied e.g. to knee or shoulder joints. The rings of the element 2 18, 28, 38 are manufactured from aluminum and each ring 18, 28, 38 is supported with three auxiliary parts 50a, 50b, 50c with three ball shaped teflon rollers 52a, 52b, 52c. A belt drive transmission is utilized to transfer power from direct drive motors 15, 25, 35 to the rings 18, 28, 38 using timing belts 11 that are respectively fixed to the aluminum rings 18, 28, 38 and aluminum pulleys 13, 23, 33 that are respectively attached to the transmission axle of each direct drive motor 15, 25, 35. In the current embodiment, the transmission ratio is set to 25 for the shoulder and 5.6 for the knee joint application.

(39) The belts 11 are placed inside the rings 18, 28, 38, such that the actuators of the robot can be located inside the rings, decreasing mechanism footprint. In contrast to direct drive actuation, belt drive provides torque amplification while simultaneously enabling concentric placement of the three rings 18, 28, 38. Belt drives are preferred due to their low cost and widespread availability with various sizes and properties. The movements of the rings 18, 28, 38 are transferred to an upper planar plane by using aluminum links 80, 90, 100 and these aluminum links 80, 90, 100 are merged with links 17, 27, 37, preferably carbon fiber tubes, via linear and rotational bearings. Finally, the carbon fiber tubes, that enable a low weight and high stiffness implementation of the end-effector mount 4, are connected to the end-effector mount 4 of the joint element 2 with 120 angle between each tube 19, 29, 39.

(40) The exoskeleton is actuated using direct-drive graphite-brushed DC motors that possess 180 mNm continuous torque output. Direct drive actuators are preferred since they are highly back-driveable. Optical encoders attached to the motors have a resolution of 2000 counts per revolution, under quadrature decoding. The robot is designed to feature a symmetric structure, such that it possesses high kinematic isotropy and can be applied to both left and right limbs.

(41) A first prototype of the self-aligning joint element has a large translational workspace, covering up to 120 mm translations along x and y axes for the shoulder or 180 mm translations along x and y axes for the knee joint application, respectively. The self-aligning joint element can also sustain infinite rotations about the perpendicular axis.

(42) FIG. 5 shows the exoskeleton attached to a human knee. Similarly, FIGS. 3A and 3B illustrate the self-aligning joint element implemented in a shoulder-elbow exoskeleton.

(43) FIG. 14 shows another embodiment of a joint element 2 that is driven via cable based actuators. The actuators (not shown) drive Bowden cables 60, 62, 64 that drive rings 18, 28, 38 in a pulley like fashion. To this end the inner cables of the Bowden cables 60, 62, 64 are guided around the outer circumference of the rings 18, 28, 38. As in the other embodiments the linear bearings 10, 20, 30 are attached to the driven rings 18, 28, 38 via links.

(44) Of course, the Bowden Cables 60, 62, 64 can be used to transfer the movements of the end-effector mount 4 to sensors or resisting elements like springs or brakes (not shown) if the exoskeleton is passively driven by the human's motion attached to it.

(45) d. Synthesis of an Impedance Controller

(46) Thanks to use of back-driveable motors and utilization of low transmission ratio, the joint self-aligning joint element 2 and thus the exoskeleton 1 is highly back-driveable. As a result, it is possible to implement a model-based open-loop impedance controller for the self-aligning joint element 2 controlling interaction forces, alleviating the need for force sensors. The overall control architecture used to control the device is depicted in FIG. 11. Note that to increase the fidelity impedances rendered by the impedance controller, the end-effector mount 4 can still be equipped with a force/torque sensor 40, 41 enabling implementation of closed-loop impedance control.

(47) In FIG. 11 q, {dot over (q)} represent the actual position and velocity of the joints, {dot over (x)} and {dot over (x)}.sub.d represent the actual and desired task space velocities, F.sub.d denotes desired forces acting on the self-aligning joint element 2, J is the self-aligning joint element Jacobian matrix, T and T.sub.d are the actual and desired actuator torques, M is the joint element mass matrix, C and are the actual and modeled centrifugal and Coriolis matrices, N and {circumflex over (N)} are u.sub.ff is the feed-forward compensation term from model-based disturbance estimator, while d represents the physical disturbances acting on the system. In the control architecture, the measured actuator velocities are multiplied with the Jacobian matrix and the actual end-effector mount velocities are obtained. The difference of the actual and desired end-effector mount velocities are fed to the impedance controller and desired forces are calculated. Then, desired forces are multiplied with the Jacobian transpose matrix and desired joint torques are obtained. The desired joint torques are added with the feed-forward torques estimated using the dynamic model of the joint element, that is, Coriolis, centrifugal and gravity matrices. Since disturbances acting on the joint element are physical and changes according to the environment, the total torque applied to the physical joint element includes these parasitic effects. If a force sensor 41 is available to measure the forces applied at end-effector mount 4, then the difference between the measured and desired values of the forces can be fed to a force controller, implementing a closed-loop controller.

(48) In order to verify the position tracking performance of the controller, it is tested using a typical trajectory for the knee joint. In particular, 90 rotation of the device is commanded simultaneously with a 15 mm translation of the rotation axis. The reference signal is commanded at a frequency of 0.5 Hz, which ensures sufficiently fast motion for knee rehabilitation. FIG. 12 depicts the tracking performance of the controllers. For the experiment presented, the RMS values of the error are calculated as 1.112% in translation and 0.006% in rotation.

(49) e. Experimental Characterization

(50) Table I presents the characterization results of a 3-RRP self-aligning joint element. Instantaneous peak and continuous end-effector mount forces along x and y directions are determined as 1 kN and 80 N, respectively. Similarly, instantaneous peak and continuous end-effector mount forces along the rotational axis are found as 170 Nm and 12.5 Nm, respectively. The end-effector mount resolutions are calculated to be 0.3252 mm along x, 0.5633 mm along y directions and 0.0031 rad on the rotational direction. The workspace of the self-aligning joint element 2 spans a range from 60 mm to 60 mm along x and y directions, while the joint element is capable of performing infinite rotations about the perpendicular axis. The stability limits for virtual wall rendering are observed as 50 kN/m along x direction, 42 kN/m along y direction and 1 kN/rad on rotation. Finally, the characterization results verify that the self-aligning joint element 2 is highly back-driveable and that can be moved with a 3 N force along x and y directions. As a result of being back-driveable, the exoskeleton 1 comprising the joint element 2 can ensure safety even under power loss.

(51) TABLE-US-00001 TABLE I CHARACTERIZATION OF THE 3-RRP SELF-ALIGNING JOINT Criteria X Y Z Inst. Peak Force 1 [kN] 1 [kN] 170 [Nm] Cont. Force 80 [N] 80 [N] 12.5 [Nm] End-Eff. Resol. 0.013 [mm] 0.022 [mm] 0.0007 [rad] Reach. Worksp. 60 to 60 [mm] 60 to 60 [mm] [rad] Virt. Wall Rend. 50 [kN/m] 42 [kN/m] 1 [kNm/rad] Back-driveability 3 [N] 3 [N] 0.25 [Nm]

(52) Similarly, table II presents the experimental characterization results of a 3-RRP knee exoskeleton. Instantaneous peak and continuous end-effector mount forces along x and y directions are determined as 246.7 N and 18.4 N, respectively. Similarly, instantaneous peak and continuous end-effector mount forces along the rotational axis are found as 38.2 Nm and 2.85 Nm, respectively. These force values have also been experimentally verified at critical points of the prescribed workspace.

(53) The values of the calculated end-effector mount resolutions, of the workspace spanned by the joint element 2, of the stability limits for virtual wall rendering and of the back-driveability correspond to those of the general characterization values (cf. above).

(54) TABLE-US-00002 TABLE II CHARACTERIZATION OF THE 3-RRP KNEE EXOSKELETON Criteria X Y Z Inst. Peak Force 246.7 [N] 213.5 [N] 38.2 [Nm] Max. Cont. Force 18.4 [N] 16 [N] 2.85 [Nm] End-Eff Resol. 0.058 [mm] 0.100 [mm] 0.0031 [rad] Reach. Worksp. 60 to 60 [mm] 60 to 60 [mm] [rad] Virt. Wall Rend. 50 [kN/m] 42 [kN/m] 1 [kNm/rad] Back-driveability 3 [N] 3 [N] 0.25 [Nm]
f. Built-In Force Sensing, Series-Elastic Actuation and Variable Impedance Actuation

(55) This section presents several design variations of the self-aligning joint element 2 of the exoskeleton 1. In particular, FIG. 8 presents an embodiment design with built in force/torque sensing, the design in FIG. 9 features series-elastic actuation and a variable-impedance design that utilizes antagonist actuation is depicted in FIG. 10.

(56) The force sensing for close-loop force/impedance control is possible by attaching a multi-axis force/torque (F/T) sensor 40, 41 to the end-effector mount 4. On the other hand, thanks to the kinematic structure of the self-aligning mechanism, other low-cost solutions can also be implemented.

(57) Firstly, instead of utilizing a multi-axis F/T sensor, low-cost, single-axis force and torque cells can be embedded to the end-effector mount 4 of the mechanism. One such embodiment with three load cells 41 (one of which is redundant) and one torque cell 40 is depicted in FIG. 8. Using the load cells 41 attached to rigid links, the task space forces acting on the robot can be easily estimated by calculating the component of the force vector along each link, while the torque applied to the end effector 5 can be measured directly using a torque cell 40.

(58) Due to sensor actuation non-collocation, there exists an inherent upper limit for the closed loop gains of explicit force control. Since the closed loop gain is determined as a combination of the stiffness of the transducer and the controller gain, for high stiffness force sensors, only low controller gains can be used in order to preserve the stability of the system. Hence, the force controller becomes slow and its disturbance response may not be ideal. Series elastic actuation (SEA) is a force control strategy that transfers the stiffness of the force sensor to the gain of the controller so that a better controller performance can be achieved. Use of an SEA for force control is advantageous, since it alleviates the need for high-precision force sensors/actuators and allows precise control of the force exerted by the actuator through typical position control of the deflection of the compliant coupling element. In particular, SEA introduces a compliant element between the actuator and the environment, then measures and controls the deflection of it. That is, an SEA transforms the force control problem into a position control problem that can be addressed using well established motion control strategies. Other benefits of SEAs include low overall impedance of the system at the frequencies above the control bandwidth which avoids hard impacts with environment. The main disadvantage of SEAs is their low control bandwidth due to the intentional introduction of the soft coupling element. The force resolution of an SEA improves as the coupling is made more compliant; however, increasing compliance decreases bandwidth of the control system, trading off response time for force accuracy.

(59) FIG. 9 presents an embodiment of the self-aligning joint element 2 with SEA. In this embodiment, a compliant element 42 is placed between the links 17, 27, 37 and output 5 of the 3-RRP mechanism and deflection of this compliant mechanism is measured as low-cost means of obtaining the forces and torques acting on the joint element 2. In particular, the compliant body 42 in the figure is designed as a 3-RRR parallel mechanism, since this mechanism allows translations in plane and a rotation along the perpendicular axis. Therefore, measuring the deflections of the compliant joints 42 that are attached to end-effector mount 4, it is possible to estimate all the forces and torques acting on the self-aligning joint 2. In particular, the fixed frame (end effector mount 4) of the compliant mechanism is attached to the rigid links 17, 27, 37 and the output of the compliant joint 42 is attached to the output of the 3-RRP mechanism (end-effector 5). The joints 42 of the compliant mechanism are designed as hinge-notch joints and the stiffness function of the joints and the task space stiffness of the compliant mechanism is derived as described in Kang (B. H. Kang, J.-Y. Wen, N. Dagalakis, and J. Gorman, Analysis and design of parallel mechanisms with flexure joints, Robotics, IEEE Transactions on, vol. 21, no. 6, pp. 1179-1185, 2005). Independent joint displacements of the compliant mechanism can be measured using linear encoders and given the joint stiffness, end-effector mount F/T can be derived. The range of the measured forces depends on the compliant joint design, while the force resolution of the system depends on the encoder resolution.

(60) While adding compliance to an actuator, different levels of stiffness are required for various interactions: Precise position control tasks with good disturbance rejection characteristics require actuators with high stiffness, while impacts can be better regulated using actuators with low stiffness. Therefore, variable stiffness actuators (VSAs) have been introduced. VSAs are special type of compliant mechanisms that feature adjustable stiffness via controlled spring like elements. While designing VSAs, it is preferable to be able to adjust stiffness independent of the configuration of the actuators. To achieve this goal, several different approaches have been proposed.

(61) The most common approach to design of variable stiffness actuators is inspired from human muscles and utilizes antagonistic actuation. In one way of designing antagonistic actuators, two motors are connected to spring like compliant elements and these compliant elements are connected to the output link. The opposite movement of these two actuators creates compression forces on one element and tension on the other. It has been shown in literature that if the force function of the springs are non-linear (in particular, if it is quadratic), this conjugate actuator movement does not affect the configuration of the output link position but changes its stiffness. Similarly, if both actuators move in the same direction, the configuration of the output link is changed preserving its stiffness.

(62) FIG. 10 depicts one sample embodiment of the variable impedance actuation for the self-aligning joint element 2. In this design, each of the three disks is composed of a combination of sub-disks 170 with special edges. The inner slots on the disks are used for the attachment of two Bowden cables 154, 164. The Bowden cables 154, 164 are working according to the antagonist principle and each cable can pull the disk up to 180. The Bowden cables are attached to non-linear springs (or more generally impedances) 152, 162 to enable mechanical variable impedance actuation via actuators 150, 160.