Journal Article10.1177/0278364908096750
Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots
97
TL;DR: This paper characterizes shortest paths for differential-drive mobile robots, with the goal of classifying solutions in the spirit of Dubins curves and Reeds—Shepp curves for car-like robots, and derives the set of optimal paths using the Pontryagin Maximum Principle.
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Abstract: The shortest paths for a mobile robot are a fundamental property of the mechanism, and may also be used as a family of primitives for motion planning in the presence of obstacles. This paper characterizes shortest paths for differential-drive mobile robots, with the goal of classifying solutions in the spirit of Dubins curves and Reeds-Shepp curves for car-like robots. To obtain a well-defined notion of shortest, the total amount of wheel-rotation is optimized. Using the Pontryagin Maximum Principle and other tools, we derive the set of optimal paths, and we give a representation of the extremals in the form of finite automata. It turns out that minimum time for the Reeds-Shepp car is equal to minimum wheel-rotation for the differential-drive, and minimum time curves for the convexified Reeds-Shepp car are exactly the same as minimum wheel-rotation paths for the differential-drive. It is currently unknown whether there is a simpler proof for this fact.
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Citations
Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey
TL;DR: Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are reviewed, and particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.
Time-optimal paths for a Dubins airplane
Hamidreza Chitsaz,Steven M. LaValle +1 more
- 01 Jan 2007
TL;DR: This model extends the Dubins car by L.E. Dubins (1957) to have altitude, which leads to Dubins airplane, and characterize the time-optimal trajectories for the system through the use of the Pontryagin Maximum Principle.
Minimizing Energy Consumption of Wheeled Mobile Robots via Optimal Motion Planning
Shuang Liu,Dong Sun +1 more
TL;DR: In this article, a new optimal motion planning aiming to minimize the energy consumption of a wheeled mobile robot in robot applications is presented. But this method is not suitable for wheeled vehicles.
180
Optimal Paths for Landmark-Based Navigation by Differential-Drive Vehicles With Field-of-View Constraints
TL;DR: This paper investigates the nature of extremal paths that satisfy the FOV constraint, and provides the complete characterization of the shortest paths for the system by partitioning the plane into a set of disjoint regions, such that the structure of the optimal path is invariant over the individual regions.
128
Energy-optimal trajectory planning for car-like robots
TL;DR: This paper studies the problem of finding optimal paths and velocity profiles for car-like robots so as to minimize the energy consumed during motion, and uses the closed-form solution for the optimal velocity profiles as a subroutine to find the minimum energy trajectories.
References
Planning Algorithms: Introductory Material
Steven M. LaValle
- 01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
7.4K
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Mathematical Theory of Optimal Processes
L. S. Pontryagin
- 01 Dec 1962
TL;DR: The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems as discussed by the authors, which can be applied in a variety of situations, including linear equations with variable coefficients.
6.4K
The Mathematical Theory of Optimal Processes
TL;DR: The Mathematical Theory of Optimal Processes (MTOP) as mentioned in this paper is a mathematical theory of optimal processes that is closely related to our approach to optimal process analysis, but with a different focus.
3.7K