Simulation of redundant manipulators for collision avoidance in manufacturing and assembly environments

A method simulating a redundant manipulator and the existing obstacle in their workspace with convex volumes in order to avoid a collision is presented. The number of convex volumes (spheres) as well as their characteristic parameters, e.g. radius and center, are determined with respect to the required accuracy of simulation. The relative position of the manipulator links are described by using the Denavit-Hartenberg homogeneous transformation matrices. Development of the kinematic equations was based on the Lagrange multiplier method in which the criterion of the obstacle avoidance is taken into account. The solution of the inverse kinematics has been obtained by numerical method. The results obtained can be checked by graphical simulation of the manipulator motion. Herewith the utilization of the increased kinematic possibilities of a redundant manipulator is enabled and the use of sophisticated jigs and fixtures in manufacturing and assembly environments can be avoided.