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Lyapunov based collision avoidance and control of multiple robots

We address the problem of path planning and control of multiple robots operating in a common workspace. The developments merge the control and trajectory planning issues for obstacle avoidance into one. We determine an online control law which avoids collisions between the arms while guiding the end-effectors from their respective starting positions S to their respective desired goal positions G, if such a collision free trajectory exists. The control law is determined from a Lyapunov function based on the total system energy. We show through simulations that this control scheme is able to guide two manipulators working in a common workspace avoid collisions with each other as they reach their goal points. No off-line path planning involving geometric analysis is necessary for this scheme to work if a collision free trajectory is feasible.