Recursive forward dynamics for multiple robot arms moving a common task object

Recursive forward dynamics algorithms are developed for an arbitrary number of robot arms moving a commonly held object. The multiarm forward dynamics problem is to find the angular accelerations at the joints and the contact forces that the arms impart to the task object. The problem also involves finding the acceleration of this object. The multiarm forward dynamics solutions provide a thorough physical and mathematical understanding of the way several arms behave in response to a set of applied joint moments. Such an understanding simplifies and guides the subsequent control design and experimentation process. The forward dynamics algorithms also provide the necessary analytical foundation for conducting analysis and simulation studies. The multiarm algorithms are based on the filtering and smoothing approach recently advanced by the author [I] for single-arm dynamics, and they can be built up modularly from the single-arm algorithms. The algorithms compute recursively the joint-angle accelerations, the contact forces and the task-object accelerations. Algorithms are also developed to evaluate in closed form the linear transformations from the active joint moments to the joint-angle accelerations, to the task-object accelerations and to the task-object contact forces. A possible computing architecture is presented as a precursor to a more complete investigation of the computational performance of the dynamics algorithms.

[1]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[2]  G. Rodriguez.  Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing , 1988 .

[3]  H. Hemami,et al.  Modeling and control of constrained dynamic systems with application to biped locomotion in the frontal plane , 1979 .

[4]  A. Morecki,et al.  Theory and Practice of Robots and Manipulators , 1985 .

[5]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[6]  Tsuneo Yoshikawa,et al.  Mechanics of coordinative manipulation by multiple robotic mechanisms , 1986, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[7]  Jens Wittenburg,et al.  Analytical Methods in Mechanical System Dynamics , 1984 .

[8]  G Rodriguez.  Recursive forward dynamics for two robot arms in a closed chain based on Kalman filtering and Bryson-Frazier smoothing , 1986 .

[9]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[10]  T. Kailath.  The innovations approach to detection and estimation theory , 1970 .

[11]  Edward J. Haug,et al.  Elements and Methods of Computational Dynamics , 1984 .

[12]  G. Rodríguez.  Spatially random models, estimation theory, and robot arm dynamics , 1987 .

[13]  Robert E. Roberson,et al.  Adaptation of a General Multibody Dynamical Formalism to Dynamic Simulation of Terrestrial Vehicles , 1976 .

[14]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[15]  H. Frisch.  A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses , 1974 .

[16]  Ronald L. Huston,et al.  Dynamics of Constrained Multibody Systems , 1984 .

[17]  Yuan F. Zheng,et al.  Computation of input generalized forces for robots with closed kinematic chain mechanisms , 1985, IEEE J. Robotics Autom..

[18]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[19]  Marc J. Richard,et al.  Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems , 1986 .

[20]  D. E. Rosenthal.  High Performance Multibody Simulations via Symbolic Equation Manipulation and Kane's Method , 1986 .

[21]  Hooshang Hemami,et al.  Modeling of Nonholonomic Dynamic Systems With Applications , 1981 .

[22]  David E. Orin,et al.  Control of Force Distribution in Robotic Mechanisms Containing Closed Kinematic Chains , 1981 .

[23]  David E. Orin,et al.  Dynamic computer simulation of multiple closed-chain robotic mechanisms , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[24]  R. Featherstone.  The Calculation of Robot Dynamics Using Articulated-Body Inertias , 1983 .

[25]  Richard H. Lathrop,et al.  Constrained (closed-loop) robot simulation by local constraint propagation , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.