A Global Cartesian Space Obstacle Avoidance Scheme for Redundant Manipulator

Optimal control of kinematically redundant manipulators involves the use of extra degrees of freedom to improve th performance by energy minimization, singularity avoidance, obstacl avoidance, higher dexterity and flexibility, etc.. Ability to avoid obstacles is important for a manipulator 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 instantaneous optimzation schemes for obstacle avoidance have been presented in the literature, which show instability, and are unable to avoid obstacles 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 Cartesian 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 self motion of the manipulator. A simulation for a three degrees of freedom planar robot is presented to demonstrate the effectiveness of the scheme.