The obstacle avoidance problem is considered 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 homogeneous 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.
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