The problem of generating an optimal feed-rate trajectory has received a significant amount of attention in both the robotics and machining literature. The typical objective is to generate a minimum-time trajectory subject to constraints such as system limitations on actuator torques and accelerations. However, developing a computationally efficient solution to this problem while simultaneously guaranteeing optimality has proven challenging. The common constructive methods and optimal control approaches are computationally intensive. Heuristic methods have been proposed that reduce the computational burden but produce only near-optimal solutions with no guarantees. A two-pass feedrate optimization algorithm has been proposed previously in the literature by multiple researchers. However, no proof of optimality of the resulting solution has been provided. In this paper, the two-pass feed-rate optimization algorithm is generalized and a proof of global optimality is provided. The generalized algorithm maintains computational efficiency, and supports the incorporation of a variety of state-dependent constraints. By carefully arranging the local search steps, a globally optimal solution is achieved. Singularities, or critical points on the trajectory, which are difficult to deal with in optimal control approaches, are treated in a natural way in the generalized algorithm. A detailed proof is provided to show that the algorithm does generate a globally optimal solution under various types of constraints. Several examples are presented to illustrate the application of the algorithm.
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June 2006
Technical Papers
A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization
J. Dong,
J. Dong
Department of Mechanical and Industrial Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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J. A. Stori
J. A. Stori
SFM Technology, Inc.
, Urbana, IL 61801
Search for other works by this author on:
J. Dong
Department of Mechanical and Industrial Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
J. A. Stori
SFM Technology, Inc.
, Urbana, IL 61801J. Dyn. Sys., Meas., Control. Jun 2006, 128(2): 379-390 (12 pages)
Published Online: July 20, 2005
Article history
Received:
August 20, 2004
Revised:
July 20, 2005
Citation
Dong, J., and Stori, J. A. (July 20, 2005). "A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization." ASME. J. Dyn. Sys., Meas., Control. June 2006; 128(2): 379–390. https://doi.org/10.1115/1.2194078
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