Minimum-time trajectories for kinematic mobile robots and other planar rigid bodies with finite control sets

Author(s):  
A. A. Furtuna ◽  
Wenyu Lu ◽  
Weifu Wang ◽  
D. J. Balkcom
2014 ◽  
Vol 47 (3) ◽  
pp. 11878-11883 ◽  
Author(s):  
Yaozhun Huang ◽  
Xuebo Zhang ◽  
Yongchun Fang

1971 ◽  
Vol 93 (3) ◽  
pp. 164-172 ◽  
Author(s):  
M. E. Kahn ◽  
B. Roth

The time-optimal control of a system of rigid bodies connected in series by single-degree-of-freedom joints is studied. The dynamical equations of the system are highly nonlinear, and a closed-form representation of the minimum-time feedback control is not possible. However, a suboptimal feedback control, which provides a close approximation to the optimal control, is developed. The suboptimal control is expressed in terms of switching curves for each of the system controls. These curves are obtained from the linearized equations of motion for the system. Approximations are made for the effects of gravity loads and angular velocity terms in the nonlinear equations of motion. Digital simulation is used to obtain a comparison of response times of the optimal and suboptimal controls. The speed of response of the suboptimal control is found to compare quite favorably with the response speed of the optimal control.


1992 ◽  
pp. 271-278 ◽  
Author(s):  
Alain Liegeois ◽  
Christophe Moignard

Author(s):  
Travis L. Brown ◽  
Tariq D. Aslam ◽  
James P. Schmiedeler

This paper addresses the problem of finding the minimum time rendezvous point for a geographically distributed group of heterogeneous mobile robots. In contrast to the traditional treatment of the multi-agent rendezvous problem, focus is given mainly to the identification of the globally optimal solution rather than the behavior of the system based on a given control policy. Level sets are introduced as a tool to solve this problem by first computing an arrival time map for each robot, subject to speed, terrain, and dynamic constraints. The computation is parallelizable by requiring each agent to generate its own arrival time map. The arrival time maps can be easily combined to give the overall minimum time rendezvous point. Despite the apparent simplicity of this approach, it is capable of accommodating numerous complicating factors with minimal modification while simultaneously generating a target path trajectory for each robot through the state-space. Examples involving ground, sea, and air robots are used to illustrate the power of this technique.


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