Time Optimal Trajectories for a Mobile Robot With Acceleration and Speed Limits in the Presence of an Obstacle

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
J. Z. Ben-Asher ◽  
E. D. Rimon ◽  
M. Wetzler ◽  
J. Diepolder
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Mobile Robot ◽  
Control Problem ◽  
Point Mass ◽  
Optimal Trajectories ◽  
Speed Limits ◽  
Optimal Paths ◽  
Time Optimal ◽  
Turn Rate

Abstract This paper studies the time optimal paths of a mobile robot navigating in a planar environment containing an obstacle. The paper considers a point-mass robot that moves with bounded acceleration and limited turn-rate controls in the presence of an obstacle. The optimal control problem yields 12 path primitives that form the time optimal paths of the point-mass robot. The problem is then extended to a disc-robot that moves in the presence of an obstacle with turn in-place capability. The optimality conditions yield 12 modified path primitives that form the time optimal paths of the disc-robot. All path primitives are analytically characterized and examples demonstrate how they form time optimal trajectories in the presence of several obstacle types.

scholarly journals Time optimal paths for high speed maneuvering

1993 ◽  
Author(s):  
D.B. Reister ◽  
S.M. Lenhart
Keyword(s):  
High Speed ◽  
Optimal Paths ◽  
Time Optimal

Time Optimal Trajectories for a Mobile Robot Under Nonsliding and Radius-of-Turn Constraints

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Joseph Z. Ben-Asher ◽  
Michael Wetzler ◽  
Elon D. Rimon
Keyword(s):  
Optimal Control ◽  
Mobile Robot ◽  
Numerical Solutions ◽  
Optimal Path ◽  
Linear Acceleration ◽  
Optimal Trajectories ◽  
Hodograph Method ◽  
Minimal Radius ◽  
Time Optimal ◽  
Target States

Abstract The time-optimal path problem for a point mass mobile robot is considered. Given initial and target states, we seek the time optimal path subject to the following constraints: (1) A limitation on its maximal linear acceleration; (2) a speed-dependent nonsliding condition; and (3) a minimal radius of turn. The paper formulates and analyzes the time optimal path problem using standard optimal control formulation with extensive use of the classical Hodograph method. Based on the analysis, the time optimal path consists of five path primitives. Numerical solutions are obtained to support and illustrate the analysis.

Time optimal steering for a mobile robot along a given path

1999 ◽  
Author(s):  
M. A. Benayad ◽  
G. Campion ◽  
V. Wertz ◽  
M. E. Achhab
Keyword(s):  
Mobile Robot ◽  
Time Optimal
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