Efficient mapping algorithms for scheduling autonomous vehicles and robotic computations

Chun-Lung Chen, Purdue University

Abstract

This research addresses the intensive computational problems of routing autonomous vehicles in a material handling system of a flexible manufacturing system (FMS) and of computing the robot inverse dynamics for servoing robot manipulators in real time. All these problems are known to be NP-complete. Various efficient scheduling and mapping algorithms are proposed to obtain fast and suboptimal or optimal solutions. The problem of optimal task (or routing) assignment of p autonomous vehicles among m workstations in a material handling system of an FMS is formulated as an equivalent problem of destinating m workstations among p autonomous vehicles. Optimization of the objective function is based on the minimax of the job execution time and the minimization of max-min of the traveling time and the min-max of the waiting time of the autonomous vehicles. Using the state-space A$\sp\*$ search algorithm, the optimal routing assignment problem has been solved both in the non-collision and the collision cases. The optimal task assignment obtained also achieves load balancing among the autonomous vehicles. The problem of scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors to achieve minimum computation time is considered. This problem is formulated as an optimal matching between a computational task graph and a processor graph. Minimizing the maximum processor finishing time is used as an objective function for the scheduling optimization. Without considering the communication costs among the processors, 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 the A$\sp\*$ algorithm coupled with an efficient heuristic function derived from the Fernandez and Bussell bound. Considering the communication costs among the processors, two efficient mapping algorithms are proposed. This mapping problem is formulated as an equivalent problem of graph partitioning and modules allocation problem. Optimization is based on the minimax of the sum of the processor finishing time and the interprocessor communication time. The first mapping algorithm utilizes the highest level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a bipartite matching algorithm. The second mapping algorithm achieves a near-optimal mapping solution by a simulated annealing method. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed scheduling/mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms.

Degree

Ph.D.

Advisors

Lee, Purdue University.

Subject Area

Electrical engineering

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