A global redundant robot control scheme for obstacle avoidance

Optimal control of kinematically redundant manipulators, thos6 with more than the minimum number of degrees of freedom required to do a specific task, is an important and complicated problem in robotics. The issue is to use the extra degrees of freedom to meet the secondary objectives such as energy optimization, singularity avoidance, obstacle avoidance, improved dynamic response, higher dexterity and flexibility, etc., in addition to the primary objective of tracking a specified path for the end-effector.

Among the secondary objectives, obstacle avoidance is important for a robot to be able to work in a cluttered environment. Using the extra degrees of freedom, we can control the redundant manipulator such that it avoids workspace obstacles and at the same time tracks the specified end-effector path. Some local optimization schemes for obstacle avoidance have been presented which are not able to avoid obstacle over long trajectories. In this paper we deal with the obstacle avoidance problem by using modern control theory and choosing an integral type performance index which results in a global optimization scheme. Obstacles are expressed as state space constraints . The state constraint function and control effort are minimized globally as a performance index. The control effort which maximizes the Hamiltonian and minimizes the performance index is used to find the homogenous solution by utilizing the null space of the Jacobian. A simulation for a three degrees of freedom planar robot is presented to demonstrate the effectiveness of the scheme.