On Computing the Global TimeOptimal Motions of Robotic Manipulators in the Presence of Obstacles

A method for computing the timeoptimal motions or robotic manipulators is presented that considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacles. Using a previously developed method for computing the timeoptimal motions along specified paths, the optimization problem is reduced to a search for the timeoptimal path in the n-dimensional position space. A small set of nearoptimal paths are first efficiently selected from a grid, using a branch and bound search and a series of lower bound estimates on the traveling time along a given path. These paths are further optimized with a local path optimization to yield the global optimal solution. Obstacles are considered by eliminating the collision points from the tessellated space and by adding a penalty function to the motion time in the local optimization. The computational efficiency of the method stems from the reduced dimensionality of the searched space and from combining the grid search with a local optimization. The method is demonstrated in several examples for two- and six-degree-of-freedom manipulators with obstacles.