Synthesis of trajectory planning using semi-algebraic sets and control of manipulators

Using semi-algebraic description of task level configuration space (TLCS) and calculus of variations, trajectory plans avoiding the otherwise invisible, TLCS obstacles, arising from the kinematic constraints due to the joint limits are synthesized. This computationally tractable trajectory planning consists of shortest and smooth geometric path planning satisfying kinematic constraints, and event-based motion planning. As opposed to the conventional algorithmic approaches to the path planning, this appealing closed form solution of the path and motion planning, and real time control is easily applicable to computer integrated manufacturing applications. The validity of this synthesis along with a real time control is demonstrated through simulation and experiment on a PUMA 560 manipulator