Efficient Scheduling Algorithms for Robot Inverse Dynamics Computation on a Multiprocessor System

The problem of scheduling the robot inverse dynamics computation consisting of m computational modules to be executed on a multiprocessor system consisting of p identical homogeneous processors to achieve a minimum-scheduled length is presented. This scheduling problem is known to be NP-complete. To achieve the minimum computation time, the Newton-Euler equations of motion are expressed in the homogeneous linear recurrence form that results in achieving maximum parallelism. To speed up the searching for a solution, a heuristic search algorithm called dynamical highest level first/most immediate successors first (DHLF/MISF) is first proposed to find a fast but suboptimal schedule. For an optimal schedule the minimum scheduled length problem can be solved by a state-space search method—the A* algorithm coupled with an efficient heuristic function derived from the Fernandez and Bussell bound. An objective function is defined in terms of the task execution time, and the optimization of the objective function is based on the minimax of the execution time. The proposed optimization algorithm solves the minimum scheduled length problem in pseudopoly nominal time and can be used to solve various large-scale problems in a reasonable time. An illustrative example of computing the inverse dynamics of an n-link manipulator based on the Newton-Euler dynamic equations is performed to show the effectiveness of the A* algorithm and the heuristic algorithm DHLF/MISF.