Two methods, time delay and trajectory modification methods for avoiding collisions between two general robot manipulators such as PUMA arms are presented.
Robots are approximated by polyhedra for the time delay method and cylinders ended by two hemispheres for the trajectory modification method. The danger of collision between two robots is represented by the distance functions defined between the robots.
In the time delay method, the collision map scheme, which can describe collisions between two robots effectively, is adopted. The minimum time delay value needed for collision avoidance can be obtained by a simple procedure of following the boundary of collision region on collision map.
In case that the time delay method is not applicable, the trajectory modification method is used. The problem of modifying trajectories to avoid collisions is formulated by an instantaneous optimization problem which minimizes a given cost function subject to physical constraints such as collision-free condition for each sampling stage. The constrained optimization problem is reformulated by an unconstrained optimization problem by the "Barrier Function" technique and to minimize the unconstrained cost function the "Conjugate Gradient" method is used. If the joint torques of robots, as a result of trajectory modification, exceed the torque limits, the dynamics of robots is scaled to meet the torque limits.
To evaluate two methods proposed, realistic simulation studies are described.
