On time-optimal feedback control

Sundar, Satish; Shiller, Zvi

doi:10.1109/acc.1994.735137

Proceedings of 1994 American Control Conference - ACC '94

DOI: 10.1109/acc.1994.735137

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On time-optimal feedback control

Satish Sundar¹,

Zvi Shiller²

Abstract: A b s t r a c t Time-optimal feedback control can be computed by solving tlie I-Iamilton-Jacobi-Belliiiaii (IIJB) equation. To date, this problem has not, been solved for nonlinear systems, such as articulat,ed robot,ic nianipulators, partly due to the difficulty in efficientsly finding a solution to tlie II.JI3 equation.In this paper, a new sufficient optiniality condition for time-optimal feedback control is present,ed. It generalizes tlie previous sufficiency condit~ions, the H J B equation and a Lyapunov-b… Show more

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Cited by 2 publications

References 11 publications

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Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation

Sundar¹,

Shiller²

Proceedings of the 1994 IEEE International Conference on Robotics and Automation

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This paper presents a mefhod for generating sh,ortest paths in cluttered envaronments, based on the Hamilton-Jaco bi-Bellman (HJB) equation.. Formulating the shortest obstacle avoidawe problem as a time optimal control problem, the shortest paths are generated by following the negative gradient of the return function, which satisfies the HJB equation. A method to generate near-optimal paths is also presented, based on a psuedo return function. Paths generated by this method are guaranteed to reach the goal, at which the psuedo return function is shown to have a un.ique minimum. The computation required t o generate the nearoptimal paths is substantially lower than those of traditional potential field methods, making it applicable to on-line obstacle avoidance. Ezamples with circular obstacles demonstrate close correlation between the near-optimal and optimal path,s, and the advantages of the proposed approach over traditional potential field methods.

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Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation

Sundar¹,

Shiller²

Proceedings of the 1994 IEEE International Conference on Robotics and Automation

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Issues in the implementation of time-optimal robot path planning

Longman

Steinbach

et al. 1997

35th Aerospace Sciences Meeting and Exhibit

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We have developed direct numerical methods of solving optimal control problems that are sufficiently fast that it is becoming reasonable to use them to perform time optimal path planning. An overview of the nature of time optimal robot motions has been developed for elbow, polar, and SCARA robots, and it has been shown that for some maneuvers a very large savings in time is possible. This offers the opportunity to increase productivity on assembly lines by making the robots more efficient in executing their point-to-point motions. This paper takes one step toward converting these time optimal results into ones that can be used in routine robot operation. Methods are developed that allow one to make the existing robot feedback controllers produce the optimal torque histories needed for time optimal operation. It is shown that this is easiest accomplished by back-computing the commands to give the robot links from the desired torque histories. (Author) AbstractThe authors and co-workers have developed direct numerical methods of solving optimal control problems that are sufficiently fast that it is becoming reasonable to use them to perform time optimal path planning. In a series of publication, a good overview of the nature of time optimal robot motions has been developed for elbow, polar, and SCARA robots, and it was shown that for some maneuvers a very large savings in time is possible. This offers the opportunity to increase productivity on assembly lines by making the robots more efficient in executing their point-to-point motions. This paper takes one step toward converting these time optimal results into ones that can be used in routine robot operation. Methods are developed that allow one to make the existing robot feedback controllers produce the optimal torque histories needed for time optimal operation. It is shown that this is easiest accomplished by back computing the commands to give the robot links from the desired torque histories.

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On time-optimal feedback control

Cited by 2 publications

References 11 publications

Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation

Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation

Issues in the implementation of time-optimal robot path planning

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