A trajectory planning of redundant manipulators based on bilevel optimization

In this paper, a novel trajectory planning approach is proposed for redundant manipulators in the case of several obstacles. The trajectory is discretized and at each step, we search for a new position of the end effector in the Cartesian space to reach the final position. Because of the redundancy, this position can be achieved by an infinity of configurations in the joint space. Thus, we use this property to find the best configuration that allows to avoid obstacles and singularities of the robot. The proposed method is based on a bilevel optimization formulation of the problem and bi-genetic algorithm to solve it. In order to avoid obstacles, we also proposed to manage constraints of the problem dynamically. This technique adapts the number of constraints in the formulation of the problem with the position of the obstacles. Simulation results showed the effectiveness of the proposed method.