Proceedings, 1989 International Conference on Robotics and Automation
DOI: 10.1109/robot.1989.100107
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Structure of minimum-time control law for robotic manipulators with constrained paths

Abstract: This paper addresses the problem of the structure of minimum-time control of robotic manipulators along a specified geometric path subject to "hard control constraints. By using the so-called "Extended Pontryagin's Minimum Principle" (EPMF' ) and a set of parameterized robot dynamic equations, it is shown that the structure of the minimum-time control law requires that one and only one control torque is always in saturation on every finite time interval along its time-optimal trajectory, while the rest of them… Show more

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Cited by 55 publications
(40 citation statements)
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References 8 publications
(10 reference statements)
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“…In the past, the early algorithms that solved the trajectory planning problem tried to minimize the time needed for performing the task (see Bobrow et al, 1985, Shin et al, 1985, Chen et al, 1989. One disadvantage of those minimum-time algorithms was that the trajectories had discontinuous values of acceleration and torques which led to dynamic problems during the trajectory performance.…”
Section: Introductionmentioning
confidence: 99%
“…In the past, the early algorithms that solved the trajectory planning problem tried to minimize the time needed for performing the task (see Bobrow et al, 1985, Shin et al, 1985, Chen et al, 1989. One disadvantage of those minimum-time algorithms was that the trajectories had discontinuous values of acceleration and torques which led to dynamic problems during the trajectory performance.…”
Section: Introductionmentioning
confidence: 99%
“…However, during the critical part of the maneuver where the robot is turning in order to avoid the obstacle, it is instead the steering torques that are saturated. Since at least one of the actuators are at its limit in each time instance, the time-optimality is implied [8]. The angular velocity profiles˙ (t) and˙ (t) are provided in Fig.…”
Section: B Experimental Resultsmentioning
confidence: 99%
“…By utilizing the special structure of the EulerLagrange model and a parametrization of the path in a path coordinate, the minimum-time problem can be reformulated to an optimal control problem with fixed horizon of the independent variable and significantly reduced number of states. Further investigations of the mentioned method with respect to singular control and model parameter uncertainties were made in [6], [7], [8]. Note that solutions to these optimal control problems were found offline.…”
Section: Introductionmentioning
confidence: 99%
“…Many efficient approaches for the time minimum trajectory planning (TMTP) problem along a predefined geometric path have been proposed, including the phase plane analysis approaches [3][4][5][6], the Pontryagin maximum principle and shooting algorithms [7], the convex optimization [2,10], the path reshaping [8], and the direct search method [9]. The recent works [2,11] are significant in which general and efficient methods are proposed.…”
Section: Introductionmentioning
confidence: 99%