METHOD OF CONTROLLING A ROBOTIZED ARM SEGMENT MAKING IT POSSIBLE TO ADAPT THE APPARENT STIFFNESS THEREOF

Abstract

The invention relates to a method of control ling an actuator (1) of an articulated segment (5) comprising the steps of estimating an inertia J of the segment; estimating or measuring a speed of displacement (I) of the segment; synthesizing a control law of type (II) generating a control torque for the segment on the basis of these estimates or measurements and meeting a performance objective pertaining to the loading sensitivity function: (III) K being the desired stiffness, and c a desired damping rate, a a mathematical artifact, (IV), where G(s) is the transfer function (V) for going between the speed (I) (linear or angular) of the segment and an external force F experienced by the segment; and controlling the actuator of the articulated segment according to the control law thus synthesized.

[00001]$\begin{array}{cc}\stackrel{.}{X}& \left(I\right)\\ H_{\infty }& \left(\mathrm{II}\right)\\ {.Math.S_F\left(s\right).Math.W_S\left(s\right).Math.}_{\infty }\le 1.Math..Math.\mathrm{avec}.Math..Math.W_s\left(s\right)={\left(\frac{J_s^2+\mathrm{.Math.}}{J_s^2+\mathrm{cs}+K}\right)}^{-1}& \left(\mathrm{III}\right)\\ S_F\left(s\right)=G\left(s\right).Math.J.Math.s& \left(\mathrm{IV}\right)\\ G\left(s\right)=\stackrel{.}{X}.Math./.Math.F& \left(V\right)\end{array}$

Claims

1. A method of controlling an actuator (1) of a hinged segment (5) including the steps of: estimating an inertia J of the segment; estimating or measuring a movement speed {dot over (X)} of the segment; synthesizing a control law of type H.sub.∞ generating a control torque for the segment on the basis of these estimates or measurements and meeting a performance objective having the effort sensitivity function: $||S_F\left(s\right).Math.W_s\left(s\right).Math.{||}_{\infty }.Math.\le 1.Math..Math.\mathrm{where}.Math..Math.W_s\left(s\right)={\left(\frac{{\mathrm{Js}}^2+s}{\mathrm{Js}+\mathrm{cs}+K}\right)}^{-1}$ K being a desired stiffness, and c a desired damping, a mathematical artifact, S.sub.F(s)=G(s).Math.J.Math.s, where G(s) is the transfer function G(s)={dot over (X)}/F between the speed X (linear or angular) of the segment and an external force F to which the segment is subjected; controlling the actuator of the hinged segment according to the control law thus synthesized.

2. The method as claimed in claim 1, wherein the control synthesis is carried out under at least one of the following constraints: a constraint with the supply current (or control torque) for the motor which must not exceed a given threshold for all of the admissible efforts. This constraint is met by the requirement that |J/F|.sub.∞23 S, where I is the strength of the current powering the motor of the actuator (or the torque required of the motor), and S is a determined threshold; a constraint relating to the positions of the poles of the control law, which poles must all be located below a threshold frequency F.sub.s less than or equal to the Nyquist frequency; a passivity constraint according to which the Speed/Force transfer transfer function $H=\frac{\stackrel{.}{x}}{F}$ must be positive-real. It is recalled that a transfer function H is positive-real if $|\frac{1-H}{1+H}.Math.{|}_{\infty }.Math.<1;$ a constraint relating to the segment+controller system sensitivity assessed at the position reference according to which: ∥S.sub.X(s)W.sub.s(s)∥.sub.∞≦1; a constraint relating to the segment+controller system sensitivity assessed at the speed reference according to which: ∥S.sub.X(s)W.sub.s(s)∥.sub.∞≦1; a constraint relating to the damping of the poles of the closed loop system according to which these poles must comply with the following inequation: $\frac{\left|\mathrm{Re}\left(p\right)\right|}{\left|p\right|}\ge \xi ,$ where Re denotes the real part of the poles.

3. The method as claimed in claim 1, wherein, in the synthesis of the control law, the stiffness K is explicitly included as a variable exogenous parameter both in the sensitivity function and in the threshold function for the purpose of performance:
∥S.sub.F(K,s)W.sub.s(K,s)∥.sub.∞≦1.

4. The method as claimed in claim 3, wherein, to solve the problem for all K.sub.min≦K≦K.sub.max, the following problems are solved simultaneously:
∥S.sub.F(K.sub.min,s)W.sub.s(K.sub.max,s)∥.sub.∞≦1 et ∥S.sub.F(K.sub.min,s)W.sub.s(K.sub.max,s)∥.sub.∞≦1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The invention will be better understood in light of the following description of a nonlimiting specific method of implementing the invention, with reference to the figures of the appended drawings wherein:

[0022] FIG. 1 is a schematic view of a comanipulator arm segment actuated by means of a cable actuator;

[0023] FIG. 2 is a graph showing the Bode plot of the segment and the threshold function;

[0024] FIG. 3 is a block diagram of the feedback control implemented by means of the invention.

DETAILED DESCRIPTION OF A METHOD OF IMPLEMENTING THE INVENTION

[0025] Referring to the figures, the invention is, in this case, used to control a hinged segment of a robot arm that can be used with comanipulation. The robot includes an actuator 1 moving a cable 2 wound about a return pulley 3 and about a hinge pulley 4 leading a segment 5 that is hinged about a hinge pin 6. In this case, the actuator includes a motor 7 associated with a reduction gear 8 which drives the nut of a ball transmission 9, the socket screw of which is connected to the cable 2 which passes inside the screw.

[0026] According to the invention, the first step is to estimate the inertia J of the hinged segment 5 about the hinge pin 6. Various methods are known for estimating such an inertia. For example, it is possible, from the definition of the segment, to add the specific inertias of all of the elements making up the segment to an inertia about the hinge pin 6 and total all of these inertias.

[0027] The method of the invention includes the step of synthesizing a control law for the actuator 1 such that the hinged segment 5 behaves as if the segment had a chosen stiffness K and was subjected to a damping c. This damping can be deduced from a damping rate ζ f by c=2Σ√{square root over (KJ)}.

[0028] For this purpose, the transfer function G(s)={dot over (X)}/F is measured, where {dot over (X)} is the speed of the hinged segment 5, and F is the external effort acting on the hinged segment 5 (for example, the weight of a load that the segment lifts). The variable s is the Laplace variable.

[0029] Using the conventional tools for the synthesis H.sub.∞, a control law is determined, the inputs of which are the speed {dot over (X)} and the output is a control torque, represented in this case by a control current (or torque) I, as is shown in the diagram of FIG. 3. The synthesis meets the following objective: ∥S.sub.p(s)W.sub.s(s)∥.sub.∞≦1, wherein the threshold is

[00004]$W_s\left(s\right)={\left(\frac{{\mathrm{Js}}^2+s}{{\mathrm{Js}}^2+\mathrm{cs}+K}\right)}^{-1},$

K being the desired stiffness, and c the desired damping, ε being a mathematical artefact intended to prevent infinite gains at low frequency. To this end, S.sub.F(s) is the segment+controller system sensitivity function assessed at the effort experienced: S.sub.F(s)=G(s).Math.J.Math.s, where J is the mass (or the inertia) of the segment. G(s) is the transfer function G(s)={dot over (X)}/F between the speed _k (linear or angular) of the segment and an external force F to which the segment is subjected.

[0030] Namely, it is required that the characteristic curve in a Bode plot of the transfer function S.sub.F(s) is below the characteristic curve of the threshold function W.sub.s(s).

[0031] Then, once the control law has been synthesized as has just been stated, this control law is used to control the actuator.

[0032] Moreover, and according to a specific aspect of the invention, at least one of the following constraints is required: [0033] a constraint with the supply current (or control torque) for the motor which must not exceed a given threshold for all of the admissible efforts. This constraint is met by the requirement that |J/F|.sub.∞≦S, where I is the strength of the current powering the motor of the actuator (or the torque required of the motor), and S is a determined threshold; [0034] a constraint relating to the positions of the poles of the control law, which poles must all be located below a threshold frequency F.sub.s less than or equal to the Nyquist frequency; [0035] a passivity constraint according to which the Speed/Force transfer transfer function

[00005]$H=\frac{\stackrel{.}{x}}{F}$

must be positive-real. It is recalled that a transfer function H is positive-real if

[00006]$|\frac{1-H}{1+H}.Math.{|}_{\infty }.Math.<1;$ [0036] a constraint relating to the segment+controller system sensitivity assessed at the position reference according to which: ∥S.sub.X(s)W.sub.s(s)∥.sub.∞≦1, where

[00007]$S_x=1-\frac{x}{x_{\mathrm{ref}}},$

with X being the position of the robot and X.sub.ref being the position reference; [0037] a constraint relating to the segment+controller system sensitivity assessed at the speed reference according to which: ∥S.sub.X(s)W.sub.s(s)∥.sub.∞≦1 where

[00008]$S_{\stackrel{.}{x}}=1-\frac{\stackrel{.}{x}}{{\stackrel{.}{x}}_{\mathrm{ref}}},$

with {dot over (X)} being the speed of the robot and {dot over (X)}.sub.ref being the speed reference; [0038] a constraint relating to the damping of the poles of the closed loop system according to which these poles must comply with the following inequation:

[00009]$\frac{\left|\mathrm{Re}\left(p\right)\right|}{\left|p\right|}\ge \xi ,$

where Re denotes the real part of the poles. The effect of this constraint is to reinforce the damping requirement expressed in the weighting function W.sub.s.

[0039] In the examples described below, the stiffness K is fixed at a determined value. However, it can be useful to vary the stiffness over time. For this purpose, and according to an alternative of the invention, this stiffness K is explicitly included as a variable exogenous parameter both in the sensitivity function and in the threshold function for the purpose of performance: ∥S.sub.P(K,s)W.sub.s(K,s)∥.sub.∞≦1.

[0040] In this formulation of the problem to be solved, K is now considered as a variable. In order to solve this problem for all K.sub.min≦K≦K.sub.max, it is sufficient to simultaneously solve the problems:

∥S.sub.F(K.sub.min,s)W.sub.s(K.sub.max,s)∥.sub.∞≦1 et ∥S.sub.F(K.sub.min,s)W.sub.s(K.sub.max,s)∥.sub.∞≦1.

[0041] The invention is not limited to the above description, but includes, on the contrary, any alternative falling within the scope defined by the claims. In par ticular, the inertial characteristics (position, speed, acceleration) of the arm segment can relate to both linear movements and angular movements.