Apparatus for unloading a user's body weight during a physical activity of said user, particularly for gait training of said user

Abstract

The invention relates to an apparatus (1) for unloading a user's body weight during a physical activity of said user (4), particularly for gait training of said user (4), comprising: a plurality of ropes (41, 42, 43, 44), wherein each rope (41, 42, 43, 44) extends from an associated drive unit (510, 520, 530, 540), is deflected by a passively displaceable deflection device, e.g. a device that is displaceable by means of the forces in the deflected ropes, and then runs to a first free end (41 a, 42a, 43a, 44a) of the respective rope (41, 42, 43, 44), and a node (60) being coupled to said first free ends (41 a, 42a, 43a, 44a) and being designed to be coupled to said user (4), wherein the drive units (510, 520, 530, 540) are designed to retract and release the respective rope (41, 42, 43, 44) so as to adjust a current rope force (FR) along the respective rope (41, 42, 43, 44), which current rope forces add up to a current resulting force (F) exerted on said user (4) via said node (60) in order to unload the user (4) upon said physical activity. Further, the invention relates to a method for controlling such a system.

Claims

1. An apparatus for unloading a user's body weight during a physical activity of the user, comprising: a rope; a deflection device; a drive unit; a node; a horizontal guide rail; a force sensor configured to determine the force on the rope; a winch; an actuator; and a sensor configured to detect the length of the rope that is free of the winch and the position of the deflection unit on the horizontal guide rail as indicators of the position of the node and, subsequently, the user, wherein the rope extends at one end from the drive unit to the deflection device, and is deflected by the deflection device, wherein the rope is coupled at its second end to the node, wherein the deflection device is slidably connected to the guide rail and is configured to be displaced by forces induced into the deflection device via the rope, wherein the node is configured to be coupled to a user, wherein the drive unit is configured to retract and release the rope to adjust the force along the associated rope, wherein the rope is connected at its first end to the winch and is configured to be wound around the winch, wherein the actuator is configured to exert a torque on the winch which effects the winding of the rope around the winch, and wherein the apparatus is configured to unload a portion of the user's body weight and to support the user during physical activity.

2. The apparatus according to claim 1, further comprising: a second rope; a second deflection device; and a second drive unit, wherein the second rope extends at one end from the second drive unit to the second deflection device, and is deflected by the second deflection device, wherein the second rope is coupled at its second end to the node, and wherein the second drive unit is configured to retract and release the second rope to adjust the force along the rope.

3. The apparatus according to claim 1, wherein the deflection device is configured to be suspended from a support frame or from a ceiling of a room.

4. The apparatus according to claim 1, further comprising a bail for coupling the node to the user, wherein the bail is rotatably connected to the node, so that the bail can be rotated about a vertical axis, wherein the bail comprises two opposing free ends, wherein each of the two free ends comprises a receptacle for receiving a connector for connecting a harness to the bail, wherein the harness is designed to be attached to the user in order to connect the user to the node via the bail, and wherein the connectors are configured to be length adjustable for adapting the apparatus to the user.

5. The apparatus according to claim 1, wherein the force sensor interacts with the rope to determine the force on the rope.

6. The apparatus according to claim 5, wherein the force sensor is connected to the node, wherein the rope is connected to the node via a spring, wherein the force sensor is configured to measure the length of the spring, wherein the force sensor comprises a cable-extension transducer having a measuring cable wound on a cylinder coupled to a shaft of a rotational sensor, and wherein the measuring cable is connected to the node end of the rope and the respective spring.

7. The apparatus according to claim 1, wherein the apparatus comprises a control unit configured to control the drive unit such that the force on the rope approaches a desired force and the position of the node is adjusted.

8. The apparatus according to claim 7, wherein the control unit is configured to control the torque exerted by the actuator onto the winch such that the force on the node and, subsequently, the user approaches a desired force, wherein the control unit is configured to control the movement of the deflection unit.

9. The apparatus according to claim 7, wherein the drive unit comprises a brake for arresting the respective winch, and wherein the drive unit comprises a presser configured to press the rope against the winch.

10. The apparatus according to claim 1, further comprising: three additional ropes; three additional deflection devices; and three additional drive units, wherein each additional rope extends at one end from one of the additional drive units to one of the additional deflection devices, and is deflected by the additional deflection device, wherein each additional rope is coupled at its second end to the node, and wherein each additional drive unit is configured to retract and release the associated additional rope to adjust the force along the rope.

11. The apparatus according to claim 10, further comprising a second horizontal guide rail.

12. The apparatus according to claim 11, wherein each of the guide rails is configured to be connected to a support structure, and wherein the guide rails run parallel to each other, wherein each guide rail is tilted relative to horizontal, about its longitudinal axis.

13. The apparatus according to claim 11, wherein two of the deflection devices are slidably connected to the first horizontal guide rail and the other two deflection devices are slidably connected to the second horizontal guide rail.

14. The apparatus according to claim 13, wherein the deflection devices each comprise a base slidably connected to the associated guide rail, and wherein each deflection device comprises an arm hinged to the base of the deflection device so that the arm can pivot relative to the base about a pivot axis running parallel to the longitudinal axis of the guide rail, and a roller connected to the arm, around which the respective rope is laid.

Description

(1) Further features and advantages of the invention shall be described by means of a detailed description of embodiments with reference to the Figures, wherein

(2) FIG. 1 shows an exemplary support frame of an apparatus according to the invention;

(3) FIG. 2 shows a perspective view of the ropes, drive units, deflection units and the moveable signal processing unit;

(4) FIG. 3 shows a perspective view of a drive unit according to FIG. 2;

(5) FIG. 4 a perspective view of the spring elements, the rope force sensors, the node and the bail of the apparatus according to the invention;

(6) FIG. 5 a perspective view of a deflection device (unit) of the apparatus according to the invention;

(7) FIG. 6 a closer perspective view of the spring elements, the node, the rope force sensors and the bail of the apparatus according to the invention,

(8) FIG. 7 a schematical, perspective view of the apparatus according to the invention when used by a user;

(9) FIG. 8 a schematical perspective view of an arresting means for arresting a deflection device of the apparatus according to the invention; and

(10) FIG. 9 another perspective view of an apparatus according to the invention.

(11) FIG. 1 shows in conjunction with FIGS. 2 to 8 an apparatus 1 according to the invention for guidedly unloading a user 2 upon a physical activity (e.g. gait training as shown in FIG. 7).

(12) The apparatus 1 comprises a suitable support structure (e.g. support frame) 10 having an upper frame part 100 being supported by a plurality of vertically extending leg members 101, such that the leg members 101 confine (together with the upper frame part 100) a three-dimensional working space 3, in which the user 4 can move along the horizontal x-y-plane (as well as vertically in case corresponding objects, e.g. inclined surfaces, staircases etc., are provided in the working space 3). Alternatively, a ceiling of a room can be used as a support structure. Said working space 3 then extends below said ceiling.

(13) The upper frame part 100 is formed by two parallel longitudinal members 102 extending along the x-direction and five parallel cross members 103 extending along the y-direction and connecting the two longitudinal members 102. The longitudinal and cross members 102, 103 span the horizontally extending upper frame part 100.

(14) A first and a second guiding rail 21, 22 are attached to the support structure 10 (e.g. to the upper frame part 100), wherein the two guide rails 21, 22 each extend along a respective longitudinal axis L, L′. The first guide rail 21 is designed to slidably support a first and a second deflection device 31, 32 as shown in FIG. 2, whereas the second guide rail 22 is designed to slidably support a third and a fourth deflection device 33, 34. Here, the first and the second 31, 32 as well as the third and the fourth deflection device 33, 34 are connected by a rigid connecting means 350, 360 so that the two pairs of deflection devices 31, 32, 33, 34 each form a deflection unit (trolley) 35, 36, which can slide along the respective guide rail 21, 22. Preferably, the guide rails 21, 22 are pivoted by an angle W=45° C. as shown in FIG. 5.

(15) As indicated in FIG. 8, each deflection device 31, 32, 33, 34 may be arrested with respect to the associated guide rail 21, 22 by means of an arresting element C. Such an element C can be a separate element providing a stop for a deflection device 31, 32, 33, 34 but may also be integrated into a deflection device 31, 32, 33, 34 and may be designed to clamp the respective deflection device 31, 32, 33, 34 to the respective guide rail 21, 22. Particularly, arrested deflection devices 31, 32, 33, 34 may be used when the apparatus 1 is used with a treadmill.

(16) Each deflection unit 35, 36 is configured to deflect two ropes 41, 42, 43, 44 as shown in FIG. 2, for instance. The individual ropes 41, 42, 43, 44 each extend from a drive unit 510, 520, 530, 540 comprising a winch 511, 521, 531, 541, respectively, on which the respective rope 41, 42, 43, 44 is wound, to an associated deflection device 31, 32, 33, 34 of the respective deflection unit 35, 36. From the deflection devices 31, 32, 33, 34 the ropes 41, 42, 43, 44 extend towards a node 60, to which a first free end of each rope 41, 42, 43, 44 is connected via a spring element 71, 72, 73, 74 as shown in FIGS. 2, 4 and 6 for instance.

(17) The mounting positions D of the individual drive units 510, 520, 530, 540 are indicated in FIG. 1. Each deflection unit 35, 36 is associated to two drive units 510, 520; 530, 540, which are positioned on either side of the respective guide rail 21, 22 along the respective longitudinal axis L, L′.

(18) In FIG. 5 a single deflection device 34 is shown (the others are constructed analogously), wherein the connecting element 360 connecting said device 34 to its neighboring counterpart (not shown) is indicated by dashed lines. The deflection device 34 comprises a base 340 that slidably engages with the respective guide rail 22 so as to allow for sliding the base 340 along the guide rail 22. A u-shaped arm 341 is pivotably hinged to two protruding regions 342, 343 of the base 340 such that the arm 341 can be pivoted about a pivoting axis A running along the x-direction (longitudinal axis L′). The arm 341 serves for bearing a deflection element 344 in the form of a roller being rotatable about a rotation axis A′, around which roller 344 the respective rope 44 is laid for deflecting the latter.

(19) In detail, as shown in FIG. 3, each drive unit 510, 520, 530, 540 comprises an actuator (servo motor) 512, 522, 532, 542 being connected via a (flexible) coupling 53 to a drive axis 55 of a winch 511, 521, 531, 541, on which the respective rope 41, 42, 43, 44 is wound. The respective winch 511, 521, 531, 541 and the respective actuator 512, 522, 532, 542 are mounted on a common platform 50, wherein two retaining elements 51, 52 protrude from the platform 50, on which elements 51, 52 the respective winch 511, 521, 531, 541 is rotatably supported. Further, the respective drive unit 510, 520, 530, 540 comprises at least one pressure roller 54 for pressing the respective rope 41, 42, 43, 44 against the associated winch 511, 521, 531, 541 so that the respective rope 41, 42, 43, 44 can be reeled an unreeled in a defined manner.

(20) The drive units 510, 520, 530, 540 interact with a sensor means (that may consist of several individual sensors, see above) that is adapted to provide output signals that represent (or can be transformed into) the length s.sub.w of (a portion of) the respective rope 41, 42, 43, 44 that is currently unwound from the respective winch 511, 521, 531, 541, the position s.sub.T of the deflection units 35, 36 along the x-direction (i.e. along the respective guide rail 21, 22), as well as the position n of the node 60 (user 4).

(21) As shown in FIG. 6, the ropes 41, 42, 43, 44 meet at the node 60, to which they are coupled via a spring element 71, 72, 73, 74, respectively. In order to be able to detect the rope forces F.sub.R (c.f. FIG. 7) currently acting along the ropes 41, 42, 43, 44 onto the node 60 and thus onto the user 4, four rope force sensors 710, 720, 730, 740 in the form of cable-extension transducers are provided on the node 60, wherein the respective measuring cable 711, 721, 731, 741 of the respective transducer 710, 720, 730, 740 is connected to the first free end 41a, 42a, 43a, 44a of the respective rope 41, 42, 43, 44 (either directly or via connection element connecting the respective spring element 71, 72, 73, 74 to the first free end 41a, 42a, 43a, 44a of the respective rope 41, 42, 43, 44) while the corresponding potentiometer 712, 722, 732, 742 is coupled to (an upper member of) the node 60. In case a spring element 71, 72, 73, 74 is elongated, the corresponding measuring cable 711, 721, 731, 741 is drawn out and the transducer (potentiometer) 710, 720, 730, 740 generates an output signal corresponding to the drawn-out length of the measuring cable 711, 721, 731, 741 corresponding to the rope force F.sub.R currently acting on the respective rope 41, 42, 43, 44 (and thereby elongating the respective spring element 71, 72, 73, 74). However, any other conceivable force sensor may be applied as well for determining the rope forces. Further, dedicated force sensors in/on the ropes 41, 42, 43, 44 can be omitted. Instead sensors for sensing the electrical current of the winch actuators 512, 522, 532, 542 can be used in order to estimate the respective winch torque. Such a sensor may be associated to each drive unit/winch 510, 520, 530, 540. Further, force sensors 710, 720, 730, 740 may be omitted in case the connecting elements are elastic, since then the rope forces can be determined from the position of the deflection devices 31. 32. 33. 34 along the guide rails 21, 22. Also in the case of non-elastic connections, at least components of the node force may be calculated from the positions of the deflection units (in the example embodiment, the node force component in x direction can be calculated purely based on positions of the trolleys, under the assumption that the trolleys have negligible dynamics such as mass and friction).

(22) Further, the node 60 comprises—with respect to an operating state of the apparatus 1—an upper node member 61, which is connected to the cable-extension transducers 710, 720, 730, 740, and a lower node member 62 being rotatably supported on the upper node member 61, so that a horizontally extending bail 80 being coupled to the lower node member 62 can be rotated about a vertical axis z.

(23) The node 60 may comprise an acceleration sensor 90 as well as a gyroscope 91 and a potentiometer 92 for sensing the acceleration of the node 60 along three orthogonal axes (for instance x, y and z), for sensing the angular velocity of the node 60 and for sensing a rotation angle of the bail 80 about said vertical axis z with respect to the upper node member 61. Further, the node may comprise a magnetometer 190 for sensing orientation of about the three axes. The acceleration sensor 90, the gyroscope 91, and the magnetometer 190 may be integrated into an integrated measuring unit (IMU) 290 providing digital output signals of the respective sensor.

(24) Corresponding output signals representing these quantities (or quantities that can be used to determine the desired quantities) are transmitted—together with the output signals from the rope force sensors 710, 720, 730, 740—via a flexible data line (cable) 93 extending from the node 60 to a movable signal processing unit 94 as shown in FIG. 2. The signal processing unit 94 is slidably supported on one of the guide rails 21, 22.

(25) The signal processing unit 94 can be driven by a further drive unit, wherein preferably the movement of the signal processing unit (also called signal box) 94 is controlled by a controlling unit 94a, to which the signal processing unit 94 is connected so that the controlling unit 94a is able to use the output signals transmitted by the signal processing unit 94 for controlling of the apparatus 1. Particularly, the controlling unit 94a is configured to control the movement of the signal processing unit 94 such that the distance between the deflection units 35, 36 or node 60 and the signal processing unit 94 along the x-direction is constant. Particularly, the movement of the signal processing unit 94 along the respective guide rail 21, 22 (x-direction) is controlled such by the controlling unit 94a that the signal processing unit is always arranged behind the node 60 (user 4) with respect to the current walking direction of the user 4.

(26) As shown in FIG. 7, the bail 80 is used for holding a harness 95 which is to be put on by the user 4. The harness 95 then supports the user 4 via two connection elements 96, 97 that are engaged with corresponding receptacles 81, 82 formed on the free ends of the bail 80, and via the node 60 to which the bail 80 is coupled.

(27) Concerning control of the current resulting force F that is exerted onto the node 60, there are many ways in classical control theory how to approach tracking problems for nonlinear systems as the present one. For example, the system could be linearized and an optimal controller could be derived. In the following, controlling is described without loss of generality for four ropes, but may also be conducted analogously for two ropes or any larger number of ropes.

(28) One idea is to control said output force vector F indirectly, by controlling individual rope forces subsumed in the vector F.sub.Rε.sup.4 in an inner loop. These rope forces F.sub.R are functions of both the device states s, i.e., the lengths s.sub.W of the unwound (portions of the) ropes 41, 42, 43, 44 (note, that the individual s.sub.W of the ropes 41, 42, 43, 44 shown in FIG. 7 may well be different from one another) and the deflection unit's 35, 36 positions x.sub.T, and the user position w:
F.sub.R=h(s,w)

(29) The three-dimensional force vector F acting on the subject 4 is given by the sum of the four individual rope force vectors F.sub.R. Therefore, there would potentially be an infinite number of solutions for rope force vectors that give the same resulting force.

(30) However, as stated above, the winch forces (torques) do not only affect rope forces, they also affect trolley (deflection unit) movement.

(31) This can be used to formulate two additional control goals, which are a) to find a solution that is also valid in static conditions (Then, the sum of forces acting on the trolleys 35, 36 will be in equilibrium, and the position can be held), and b) to have the trolleys 35, 36 move in a similar way, so that they are always at the same position x (c.f. FIG. 7). For example, if a purely vertical force is desired and the person 4 is standing in the middle between the two linear guide rails 21, 22, the trolleys 35, 36 should be positioned such that the person 4 stands below the center of a square spanned by the pulleys (deflection devices) 31, 32, 33, 34.

(32) The first goal can be formulated mathematically by requiring that in static conditions, where all speeds and accelerations are zero,
ds.sub.W/dt=0,d.sup.2s.sub.W/dt.sup.2=0,dx.sub.T/dt=0,d.sup.2x.sub.T/dt.sup.2=0,dw/dt=0,d.sup.2w/dt.sup.2=0,
the correct force is applied on the user (object) 4, i.e. the current resulting force (output force) F of the controlling unit (controller) matches the desired resulting force F.sub.des meaning equation F=F.sub.des is fulfilled. The requirement is found by force equilibrium on the two trolleys 35, 36.

(33) In summary, this yields 3 equations from force equilibrium on the node 60, further 2 equations from force equilibrium on the two trolleys 35, 36 in x-direction, and one equation commanding the two trolleys 35, 36 to be at the same position x.sub.T in x-direction. These 6 equations can be used to find the four desired rope forces F.sub.R,des and the two trolley positions.

(34) Appropriate measures (for example saturations) can be taken to make sure the ropes 41, 42, 43, 44 always remain in tension.

(35) The desired rope forces F.sub.R can then be used as a reference for the individual feedback loops for each winch 511, 521, 531, 541.

(36) For example, the control law could be
u=i(F.sub.R,des+K.sub.r(F.sub.R,des−F.sub.R))+u.sub.ff,
with F.sub.R,des being the calculated desired (reference) rope forces, i the transmission ratio of the actuator-winch unit (drive unit) 510, 520, 530, 540, K.sub.rε.sup.4×4 being a positive definite rope force feedback matrix containing feedback gains, and u.sub.ff denoting potential additional terms that go to zero in static conditions. The first two terms will ensure that the system asymptotically approaches the desired forces on the person 4, at least when the person 4 stands still.

(37) In order to make the system react fast in dynamic conditions, the terms u.sub.ff can be used. One possibility is to use a type of “synergy control”, where actuators 512, 522 532, 542 work in groups. For example, using a diagonal feedback matrix K.sub.Cε.sup.3×3, a virtual input vector u* in Cartesian space can be generated:
u*=K.sub.C(F.sub.des−F)ε.sup.3

(38) This three-dimensional vector u* then needs to be mapped to the four winch torques u by a function ρ:
u=ρ(u*).

(39) Similar to human muscles, this function could encode synergies, which lump actuators 512, 522, 532, 542 into functional groups.

(40) For example, if the force component acting on the user 4 in vertical direction z is too low compared to the reference, so u*.sub.z>0, all four winches 511, 521, 532, 541 could be pulling equally, which means that the vertical component u*.sub.z would simply be commanded to all winches 511, 521, 532, 541 equally. The component in x-direction, which is parallel to the guide rails 21, 22, could be distributed such that the winches on one side (depending on the sign, these could be 511 and 531, cf. FIG. 2) act as a pair and both pull equally, whereas the opposite pair 521, 541 does not produce additional torques. Necessary corrections in the direction orthogonal to the guide rails 21, 22 could be distributed in an analog manner, with either the winch pair 511, 521 or 531, 541 pulling, depending on the sign. This type of control law leads to a fast correction of the forces acting on the user (object) 4, and it also accelerates the movement of the passive trolleys 35, 36 towards their “ideal” asymptotic positions. In static conditions, this part of the controller will not generate any torques u.

(41) According to another embodiment illustrated in FIG. 9 In the chosen right-handed Cartesian coordinate system, z points upward and x points forward in the default gait direction, parallel to the guide rails 21, 22. As the joints in the node 60 ensure that only forces are transmitted, the harness can be represented by a single cable that connects the node to a specific point w=(w.sub.x,w.sub.y,w.sub.z).sup.T on the human (cf. FIG. 7).

(42) A state vector is assembled that describes the current positions and velocities of the device components. Given the current position vector w of the human, the configuration is fully described by be the length of ropes that have been released from each winch 511, 521, 531, 541 subsumed in the vector s.sub.Wε.sup.4:
s.sub.W=(s.sub.as.sub.bs.sub.cs.sub.d).sup.T,  (1)
and by the positions of the deflection units 35, 36, subsumed in the vector x.sub.Tε.sup.2:
x.sub.T=( x.sub.T,abx.sub.T,cd).sup.T.  (2)

(43) The state vector sε.sup.12 contains these variables and their derivatives:
s=(s.sub.W.sup.Tx.sub.T.sup.T{dot over (s)}.sub.W.sup.T{dot over (x)}.sub.T.sup.T).sup.T  (3)

(44) We now assume that the force vector F.sub.n on the user (“n” stand for the node; the force vector is also denoted shortly F) acting on the user 4 is to be controlled while the user moves. Node position is n=(n.sub.x,n.sub.y,n.sub.z).sup.T. Cable (i.e. rope) forces are subsumed in the vector F.sub.rε.sub.+ (note, that the rope forces are also denoted as F.sub.R) with
F.sub.r=(F.sub.aF.sub.bF.sub.cF.sub.d).sup.T  (4)
and the Cartesian force vector F.sub.nε.sup.3 on the user 4 is
F.sub.n=(F.sub.nxF.sub.nyF.sub.nz).sup.T  (5)

(45) Force equilibrium on the node 60 maps cable forces to forces F.sub.n acting on the user 4:
F.sub.n=J( x.sub.T,n)F.sub.r.  (6)

(46) The mapping J can be computed in an efficient way by first summing the rope forces within the two planes spanned by the ropes, via the matrix R, to obtain the x component and the force components F.sub.ab and F.sub.cd, and then converting these to Cartesian space via the matrix S:

(47) $\begin{array}{cc}J=\left(\begin{array}{cc}1& 0\\ 0& S\end{array}\right)R\mathrm{with}& \left(7\right)\\ S=\left(\begin{array}{cc}-\cos {\phi }_{\mathrm{ab}}& \cos {\phi }_{\mathrm{cd}}\\ \sin {\phi }_{\mathrm{ab}}& \sin {\phi }_{\mathrm{cd}}\end{array}\right),& \left(8\right)\\ R=\left(\begin{array}{cccc}\cos {\phi }_a& -\cos {\phi }_b& \cos {\phi }_c& -\cos {\phi }_d\\ \sin {\phi }_a& \sin {\phi }_b& 0& 0\\ 0& 0& \sin {\phi }_c& \sin {\phi }_d\end{array}\right).& \left(9\right)\end{array}$

(48) Current deflection unit 35, 36 positions x.sub.T and the node position n define the angles in these matrices.

(49) The movement of the deflection units 35, 36 is governed by the equations of motion:
m.sub.T{umlaut over (x)}.sub.T=TF.sub.r  (10)
with

(50) $\begin{array}{cc}T=\left(\begin{array}{cc}\cos {\phi }_a-1& 1-\cos {\phi }_b\\ \cos {\phi }_c-1& 1-\cos {\phi }_d\end{array}\right)& \left(11\right)\end{array}$

(51) The equations of motion for the winches 511, 521, 531, 541 are given by:
m.sub.W{umlaut over (s)}.sub.W=F.sub.r−F.sub.W,  (12)
with the winch actuator forces F.sub.W (e.g. the torques multiplied by a transmission ratio i). The rope forces are a linear function of the spring deflections of the springs 71, 72, 73, 74 (cf. FIG. 6):
F.sub.r=c.sub.F(−s.sub.W+Gx.sub.T−l)  (13)
with the matrix

(52) $\begin{array}{cc}G=\left(\begin{array}{cc}1& 0\\ -1& 0\\ 0& 1\\ 0& -1\end{array}\right)& \left(14\right)\end{array}$
and the vector l containing the distances from the four deflection devices 31, 32, 33, 34 to the node 60 (vector n). To avoid offsets in these equations, the rope lengths s.sub.W are defined appropriately.

(53) Even without force sensors, it is still possible to implicitly measure the force in x direction, by means of deflection device 31, 32, 33, 34 positions. Assuming that the mass of the deflection devices 31, 32, 33, 34 is negligible, their positions are determined by the components of the cable forces acting in x direction: Static equilibrium on the deflection device 31, 32, 33, 34 is given by setting (10) to zero. Combined with (6), the force in x direction is then given by:

(54) $\begin{array}{cc}{F}_{\mathrm{nx}}=F_{\mathrm{ab}}\frac{\cos {\phi }_b-\cos {\phi }_a}{\sin {\phi }_a-\sin \left({\phi }_a+{\phi }_b\right)+\sin {\phi }_b}+F_{\mathrm{cd}}\frac{\cos {\phi }_d-\cos {\phi }_c}{\sin {\phi }_c-\sin \left({\phi }_c+{\phi }_d\right)+\sin {\phi }_d}& \left(15\right)\end{array}$

(55) These angles are calculated based on geometry only (rope lengths, deflection device positions). To keep the estimation robust, F.sub.ab and F.sub.cd are taken preferably as the desired, not the actual values, even if force sensors are available.

(56) Now, an ideal controller would command actuator torques u, so that the outputs match the desired force vector F.sub.n,des that acts on the subject (also denoted as user) 4:
F.sub.nF.sub.n,des,  (16)
regardless of the movement of the subject 4. Preferably, a force controller (provided by the controlling unit) is used in Cartesian space, which commands a Cartesian force vector .sup.CF.sub.fc that is to be realized by the winches. This force is calculated by PI (proportional-intergral) control and feedforward of the reference:

(57) $\begin{array}{cc}{}^{C}F_{\mathrm{fc}}=F_{n,\mathrm{des}}+\left(K_P+\frac{K_I}{s}\right)\left(F_{n,\mathrm{des}}-F_n\right),& \left(17\right)\end{array}$
with s being the Laplace operator, K.sub.P being a positive definite matrix of proportional gains, and K.sub.I being a positive definite matrix of integral gains.

(58) Cartesian forces need to be mapped to winch forces F.sub.w, which is the inverse problem of (6). Given that there are four winch forces and only three node force components, there are multiple solutions to (6) with a given node force. If the deflection devices 31, 32, 33, 34 were not movable, quadratic programming could be used to find the minimal cable forces that fulfill the constraints. However, in the current system, the rope forces do not only influence the output force vector, but they also influence the movement of the deflection devices 31, 32, 33, 34, according to (10). In turn, the position of the deflection devices 31, 32, 33, 34 defines the polygon of applicable forces.

(59) Therefore, instead of minimizing rope forces, one may take deflection device dynamics into account to solve the rank deficiency in the inverse mapping of (6). The idea is that rope forces are applied in such a way that the deflection devices 31, 32, 32, 34 stay together, leading to a polygon with rectangular base. This behavior is enforced by the law:
m.sub.T({umlaut over (x)}.sub.T,ab−{umlaut over (x)}.sub.T,cd)−k.sub.T( x.sub.T,ab−x.sub.T,cd)  (18)
with the positive constant k.sub.T.

(60) With (10), this yields
F.sub.a(1−cos φ.sub.a)−F.sub.b(1−cos φ.sub.b)−F.sub.c(1−cos φ.sub.c)+F.sub.d(1−cos φ.sub.d)k.sub.T(x.sub.T,ab−x.sub.T,cd)  (19)

(61) Using this additional constraint on the forces, the control law maps desired forces in Cartesian space to winch forces, such that they work in synergy:

(62) $\begin{array}{cc}{F}_w=R^{\prime -1}\left(\begin{array}{c}\left(\begin{array}{cc}1& 0\\ 0& S^{-1}\end{array}\right){}^{C}F_{\mathrm{fc}}\\ k_T\left(x_{T,\mathrm{ab}}-x_{T,\mathrm{cd}}\right)\end{array}\right)& \left(20\right)\end{array}$
with the desired reference force in Cartesian space F.sub.n,des and the modified mapping matrix

(63) $\begin{array}{cc}{R}^{\prime }=\left(\begin{array}{c}R\\ r^{\prime T}\end{array}\right),& \left(21\right)\end{array}$
With
r′.sup.T=(1−cos φ.sub.a cos φ.sub.b−1 cos φ.sub.c−1 1−cos φ.sub.d).   (22)

(64) In the above, one may calculate the force in x direction as a linear combination (for example the mean value) of spring-based measurement and deflection device-based measurement.