Generalized Multi-Speed Dubins Motion Model

2024-02-02

IEEE Transactions on robotics

AI Summary

To address the suboptimal path planning, excessively large turning radii, and high collision risk near obstacles exhibited by the classical Dubins model under multi-speed scenarios, this paper proposes the Generalized Multi-Speed Dubins Motion Model (GMDM). GMDM is the first Dubins-based framework to incorporate dynamic speed variation while preserving analytical tractability and relaxing the constant-speed constraint. Theoretically, GMDM guarantees full configuration-space reachability and reduces to the standard Dubins model under uniform speed. Leveraging an extended taxonomy of six path topologies, it integrates piecewise speed modeling with analytic geometric derivation to enable real-time computation. Experimental results demonstrate that GMDM achieves travel times nearly optimal in obstacle-free environments and significantly reduces collision probability in high-density obstacle fields, while maintaining computational overhead comparable to the original Dubins model.

Technology Category

• Planning, Routing, and Scheduling: Model-Based Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The paper develops a novel motion model, called Generalized Multi-Speed Dubins Motion Model (GMDM), which extends the Dubins model by considering multiple speeds. While the Dubins model produces time-optimal paths under a constant speed constraint, these paths could be suboptimal if this constraint is relaxed to include multiple speeds. This is because a constant speed results in a large minimum turning radius, thus producing paths with longer maneuvers and larger travel times. In contrast, multi-speed relaxation allows for slower speed sharp turns, thus producing more direct paths with shorter maneuvers and smaller travel times. Furthermore, the inability of the Dubins model to reduce speed could result in fast maneuvers near obstacles, thus producing paths with high collision risks. In this regard, GMDM provides the motion planners the ability to jointly optimize time and risk by allowing the change of speed along the path. GMDM is built upon the six Dubins path types considering the change of speed on path segments. It is theoretically established that GMDM provides full reachability of the configuration space for any speed selections. Furthermore, it is shown that the Dubins model is a specific case of GMDM for constant speeds. The solutions of GMDM are analytical and suitable for real-time applications. The performance of GMDM in terms of solution quality (i.e., time/time-risk cost) and computation time is comparatively evaluated against the existing motion models in obstacle-free as well as obstacle-rich environments via extensive Monte Carlo simulations. The results show that in obstacle-free environments, GMDM produces near time-optimal paths with significantly lower travel times than the Dubins model while having similar computation times. In obstacle-rich environments, GMDM produces time-risk optimized paths with substantially lower collision risks.

Problem

• Extends Dubins model to optimize paths with multiple speeds
• Reduces travel time and collision risk in motion planning
• Provides analytical solutions for real-time path optimization

Innovation

• Extends Dubins model with multiple speed options
• Enables joint optimization of time and risk
• Provides analytical solutions for real-time use