Joint-Space Orthogonalization and Passivity for Physical Interpretations of Dextrous Robot Motions Under Geometric Constraints

A principle of ‘joint-space orthogonalization’ is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric constraints. The principle realizes the hybrid control in a strict sense by letting position feedback signals be orthogonal in joint space to the contact force vector whose components exert at corresponding joints. This orthogonalization is executed via a projection matrix computed in real-time from a Jacobian matrix of the constraint equation in joint coordinates. To show the important role of the principle in control of robot manipulators, two basic set-point control problems are analysed. One is a hybrid PID control problem for robot manipulators under geometric endpoint constraint and another is a coordinated control problem of two arms. It is shown that passivity properties of residual dynamics of robots follow from the introduction of a quasi-natural potential and the joint-space orthogonalization. Various stability problems of PID-type feedback control schemes without compensating for the gravity force and with or without use of a force sensor are discussed from passivity properties of robot dynamics with the aid of the hyper-stability theory.

[1]  Suguru Arimoto,et al.  A New Feedback Method for Dynamic Control of Manipulators , 1981 .

[2]  John J. Craig,et al.  Hybrid position/force control of manipulators , 1981 .

[3]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[4]  Danwei Wang,et al.  Linear feedback control of position and contact force for a nonlinear constrained mechanism , 1990 .

[5]  Roberto Horowitz,et al.  Stability and Robustness Analysis of a Class of Adaptive Controllers for Robotic Manipulators , 1990, Int. J. Robotics Res..

[6]  Joseph Duffy,et al.  The fallacy of modern hybrid control theory that is based on "orthogonal complements" of twist and wrench spaces , 1990, J. Field Robotics.

[7]  Alessandro De Luca,et al.  Zero Dynamics in Robotic Systems , 1991 .

[8]  Daniel E. Koditschek,et al.  Comparative experiments with a new adaptive controller for robot arms , 1991, IEEE Trans. Robotics Autom..

[9]  Takashi Tsubouchi,et al.  Principle of Orthogonalization for Hybrid Control of Robot Manipulators , 1993, Robotics, Mechatronics and Manufacturing Systems.

[10]  Yunhui Liu,et al.  Model-based adaptive hybrid control for geometrically constrained robots , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[11]  D. Wang,et al.  Position and force control for constrained manipulator motion: Lyapunov's direct method , 1993, IEEE Trans. Robotics Autom..

[12]  Suguru Arimoto,et al.  A Class of Quasi-Natural Potentials and Hyper-Stable PID Servo-Loops for Nonlinear Robotic Systems , 1994 .

[13]  Yunhui Liu,et al.  Model-based adaptive hybrid control for manipulators with geometric endpoint constraint , 1994, Adv. Robotics.

[14]  Suguru Arimoto,et al.  Fundamental problems of robot control: Part II A nonlinear circuit theory towards an understanding of dexterous motions , 1995, Robotica.