Motion Planning and Control of Cooperative Robotic Systems

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Desai, Jaydev P.

This thesis addresses the problem of motion planning for cooperative robotic systems. The problem of motion planning for a robotic system is stated as: Given initial positions and orientations and goal positions and orientations for a collection, C, of robots, in workspace, W, generate a continuous trajectory for C avoiding contact with the obstacles, Oi, subject to various dynamical constraints of the system. Because robots are physical systems subject to continuous laws of motion and driven by continuous actuators, we formulate the motion planning problem as an unconstrained variational problem using tools from optimal control and calculus of variations in the first part of the thesis. We develop a general framework for solving motion planning problems involving equality and inequality constraints. In the second part of the thesis, we study planar human manipulation and develop a computational model for friction-assisted dual arm manipulation tasks incorporating the dynamics of the musculo-skeletal system. We show that our computational model predicts the force distribution and object trajectory in voluntary, relaxed movements. We further study similar tasks in the vertical plane and our experimental findings suggest that there is a great degree of repeatability in trajectories and velocity profiles across trials and subjects. In the third part, we focus on extending this computational model to plan and control cooperative robotic systems. We solve the dynamic motion planning problem for a system of cooperating robots in the presence of geometric and kinematic constraints, and test the resulting open-loop trajectories on the experimental testbed. In the last part of the thesis, we explore the application of the motion planning algorithms when the number of robots in C is very large. Because of increased computational time, we use optimal sensor-based closed loop motion plans. These are combined with the framework of graph theory and optimal control to guarantee provable measure on the performance of the entire system. The main contributions of the thesis are: (a) studying trajectory generation and force distribution in human dual arm manipulation; and (b) a set of motion planning algorithms for cooperating robot systems subject to dynamic constraints.

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University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-98-27.
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