On-line trajectory optimization for kinematically redundant robot-manipulators and avoidance of moving obstacles

Novel concepts are presented and verified for real-time dynamics trajectory optimization of kinematically redundant manipulators. The considered task of trajectory planning is to follow a moving target in three-dimensional work space. Hereby, the manipulator has to autonomously preserve explicitly formulated kinematic constraints such as moving obstacle avoidance and box-constraints on joint positions as well as dynamic constraints like box-constraints on joint velocities, accelerations and motor torques. The key idea is to transform the resulting overall motion planning problem into a timed series of variational problems, which, in turn, may be formulated as parameter optimization problems, that can be efficiently solved in real-time by the numerical method of sequential quadratic programming. Since the approach does not require an inverse kinematics formulation it is feasible for manipulators with redundant kinematics. The feasibility of the approach has been verified by example of a ten-degrees-of-freedom manipulator model