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TECHNICAL PAPERS

A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization

[+] Author and Article Information
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 61801

J. Dyn. Sys., Meas., Control 128(2), 379-390 (Jul 20, 2005) (12 pages) doi:10.1115/1.2194078 History: Received August 20, 2004; Revised July 20, 2005

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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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 2

Representative feed-rate profile during forward pass (left) and backward pass (right) of algorithm

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Figure 3

An airfoil-type contour in the x-y plane

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Figure 4

Feed-rate optimization results for trajectory shown in Fig. 3. Top row: case with only velocity and acceleration constraints. Middle row: addition of contour error, bandwidth, and material remove rate (MRR) constraints. Bottom row: addition of an infeasibility island on the phase plane. Left column: Feasibility boundary (thin solid line) and feed-rate profiles after sequential passes of the algorithm (indicated by numbers 1,2,3). Right column: time plot of velocity, acceleration, and parametric velocity (solid line is tangential, dashed is x axis, dotted is y axis).

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Figure 5

Example of circle contour with large radius (top) and small radius (bottom). Left column: feasibility boundary (thin solid line) and feed-rate profiles after sequential passes of the algorithm (indicated by numbers 1,2). Right column: time plot of velocity, acceleration, and parametric velocity (solid line is tangential, dashed is x axis, dotted is y axis).

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Figure 6

An example 2D tool path on x-y plane

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Figure 7

Application result for an actual 2D tool path. Left: final feed-rate profile (dashed line) on phase plane. Right: time plot of velocity, acceleration, and parametric velocity (solid line is tangential, dashed is x axis, dotted is y axis).

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Figure 8

A robot used in (2) with extensory and rotational joints

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Figure 9

Example from (2) to verify bidirectional algorithm. Left column: trajectory generated by bidirectional algorithm (switching points marked as square). Right column: trajectory generated by the algorithm from (2) (out result overlapped with circle marked curve). Top row: low friction case. Bottom row: high friction case.

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Figure 1

Boundary from acceleration limit (left) and acceleration-velocity limit (right) on phase plane

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