Robust high-performance control for robotic manipulators

A robotic system that combines model-based and performance-based techniques to control a manipulator by a control signal developed in response to input command terms including desired manipulator position, velocity, and/or acceleration as individual command input terms for the system, and wherein said control signal is formed from nominal and complement control-signal components;

• said system comprising;
• feedforward circuit means, model-based and containing a priori information concerning the manipulator's dynamics, as input into said feedforward circuit means by an operator of said system, for controlling said manipulator by a nominal signal component delivered by the feedforward circuit means to said manipulator;
• feedback circuit means, performance-based and responding to actual performance of said controlled manipulator, for emitting a feedback related signal complement which combines with said nominal signal component from said feedforward circuit means in order to form a combined control signal, which combined control signal controls said manipulator's performance;
• and said feedforward circuit means further includes;
• computation elements that receive said priori information about the manipulators dynamics as input by said operator and responds to such information and to the desired command input terms for computing partial information for on-line control over said manipulator by said nominal signal as developed by said feedforward means;
• and
• an actuator for said manipulator, and wherein the manipulator-plus-actuator has a given configuration, speed of motion, and a payload mass which is expressed as integrated dynamic model defined as;
• M(m,.theta.).theta.+N(m,.theta.,.theta.)=V
• wherein the above-noted terms are defined as
• M(m,.theta.)=G+EM*(m,.theta.);
• N(m,.theta.,.theta.)=C.theta.+EN*(m,.theta.,.theta.)
• and m is the payload mass, M*(m,.theta.) is the symmetric positive-definite n.times.n inertia matrix, N*(m,.theta.,.theta.) is the n.times.1 vector representing the total torque due to Coriolis and centrifugal term, gravity loading term, and frictional term, and the elements of M* and N* are highly coalex nonlinear functions which depend upon the configuration .theta., the speed of motion .theta., and, G and C respectively, are the inertia term and damping term for the payload mass m of said manipulator-plus-actuator.

A method of robotic control in which an on-line control over a manipulator has been initially established by a model-based control signal, the improvement comprising the steps of

• complementing said model-based control signal with another signal developed by a feedback circuit means;
• developing error signals each indicating the difference between the desired and actual manipulator velocity and position, with each error signal subject to an adaptation law which includes variable gain for each error signal in order to develop said complement signal component;
• and
• expressing said adaptation law as r(t) which is the n.times.1 vector of "weighted" position-velocity error defined by:
• r(t)=W.sub.p e(t)+W.sub.v e(t) ##EQU36## and wherein {.gamma..sub.1,.alpha..sub.1,.beta..sub.1 } are zero or positive proportional adaptation gains, {.gamma..sub.2,.alpha..sub.2,.beta..sub.2 } are positive integral adaptation gains, and W.sub.p =diag.sub.i (W.sub.pi) and W.sub.v =diag.sub.i (W.sub.vi) are constant n.times.n matrices which contain the position and velocity weighting factors for all joints of said manipulator.

In a controller having a control signal which controls a manipulator's position and velocity in Cartesean space, wherein the manipulator and environment form a system exhibiting nonlinear dynamics and system parameters which may not be fully known to an operator and wherein the controller includes an adaptive feedback servo control loop which senses actual position and velocity of said manipulator being controlled in Cartesian space, the improvement comprising:

• manipulator driving means responsive to said control signal for driving said manipulator in said environment to achieve, in Cartesean space, a desired position, velocity, and acceleration as indicated by said control signal;
• a model-based feedforward loop outside of said adaptive servo control loop that allows the operator to provide a nominal signal to the manipulator based upon a limited amount of knowledge concerning the manipulator and/or the system which the operator may elect to input into said system;
• and
• adaptive control means in said feedback servo control loop, responsive to said sensed position and velocity, for varying said control signal applied to said manipulator's driving means, which variable control signal compensates in real-time for the system's nonlinearities as said manipulator is driven in Cartesean space to a controlled position and velocity.

In a controller having a control signal which controls a manipulator's position and velocity in Cartesean space, wherein the manipulator and its environment form a system exhibiting nonlinear dynamics and system parameters which may not be fully known to an operator, and wherein the controller includes an adaptive feedback servo control loop which senses actual position and velocity of said manipulator being controlled in Cartesian space, the improvement comprising:

• manipulator driving means responsive to said control signal for driving said manipulator in said environment to achieve, in Cartesean space, a desired position, velocity, and acceleration as indicated by said control signal;
• a model-based feedforward loop separate and distinct from said adaptive servo control loop that allows the operator to provide a nominal signal to the manipulator based upon a limited amount of knowledge concerning the manipulator and/or the system which the operator may elect to input into said system;
• adaptive control means in said feedback servo control loop, responsive to said sensed position and velocity, for varying said control signal applied to said manipulator's driving means, which variable control signal compensates in real-time for the system's nonlinearities as said manipulator is driven in Cartesean space to a controlled position and velocity;
• and further wherein the system operates in real-time control with a given sampling rate, and said system further comprises;
• a feedforward computational element connected in said feedforward loop for receiving operator-input values concerning said manipulator and/or system's dynamics in order to develop a nominal signal that is applied to said control signal for said manipulator independently of said adaptive controlling means in said separate and distinct feedback control loop;
• and
• said adaptive control means operates in accordance with a control law which may be considered as though it was applied directly to the manipulator's end effector in Cartesian space, and said controller further comprises:
• means connected in a force feedforward control loop for receiving a feedforward signal representing a desired mathematical term for said manipulator;
• an adaptive proportional-integral-differential (PID) controller in said feedback control loop;
• and
• a plurality of variable gain circuits for implementing a control law characterized as an adaptive feedback controller described by
• Y.sub..alpha. (t)=f(t)+K.sub.p (t)e(t)+K.sub.v (t)e(t)
• where V.sub..alpha. (t) is the n.times.1 adaptive control voltage vector, e(t)=.theta..sub.r (t)-.theta.(t) is then n.times.1 position tracking-error vector, f(t) is an n.times.1 auxiliary signal generated by the adaptation scheme, and {K.sub.p (t),K.sub.v (t)} are n.times.n adjustable PD feedback gain matrices.

A combined model-based and performance-based robotic control system that generates a combined control signal developed from nominal and complement signal components and which exhibits noise in the form of destabilization in the control system, which noise is compensated for by .sigma.-modified law, and wherein said system is characterized in that:

• means, model-based and containing a priori information known by an operator concerning a manipulator's dynamic, connected in a feedback circuit for developing said nominal signal component;
• adaptive control means, performance-based and responding adaptively to actual performance of said controlled manipulator, for combining said complement signal generated by said adaptive control means with said nominal signal so that the combined signal controls said manipulator;
• and
• noise compensating means in the feedback means including said .sigma.-modified control law that is expressed by:
• ##EQU41## where .sigma. is a positive scalar design parameter, .mu.1 and .mu.2 are scalar adaptation gains, r is the weighted tracking error, s' is the transportation of s, where s stands for the signal on which k is acting.