SCTOMP: Spatially Constrained Time-Optimal Motion Planning (2210.02345v2)

Abstract: This paper focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows the system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the assumption that a collision-free geometric reference is given. Instead, we present a two-stage motion planning method that solely relies on a goal location and a geometric representation of the environment to compute a time-optimal trajectory that is compliant with system dynamics and constraints. To do so, the proposed scheme first computes an obstacle-free Pythagorean Hodograph parametric spline, and second solves a spatially reformulated minimum-time optimization problem. The spline obtained in the first stage is not a geometric reference, but an extension of the environment representation, and thus, time-optimality of the solution is guaranteed. The efficacy of the proposed approach is benchmarked by a known planar example and validated in a more complex spatial system, illustrating its versatility and applicability.

• The paper presents a novel three-stage planning framework that optimizes trajectory time while adhering to spatial constraints.
• It introduces closed-form PH spline generation for collision-free corridor navigation without relying on pre-defined geometric paths.
• Experimental validation on autonomous cars and quadrotors demonstrates the framework’s robustness and real-time applicability.

Overview of "SCTOMP: Spatially Constrained Time-Optimal Motion Planning"

The paper titled "SCTOMP: Spatially Constrained Time-Optimal Motion Planning" by Jon Arrizabalaga and Markus Ryll introduces a novel methodology for motion planning that optimizes trajectory time within predefined spatial constraints. Unlike traditional approaches that rely on a pre-defined collision-free geometric reference, this methodology autonomously computes trajectories using only initial and target positions along with a geometric environment model. The primary contribution is a three-stage planning framework designed to ensure time optimality while adhering to system constraints.

Methodological Framework

The approach, known as SCTOMP (Spatially Constrained Time-Optimal Motion Planner), is divided into three main stages:

1. Navigation Corridor Identification: This initial stage involves delineating collision-free corridors within the environment. This is achieved without reliance on pre-established geometric paths, enhancing flexibility and applicability in complex environments.
2. Path Spline Calculation: Once corridors are identified, the second stage involves creating a Pythagorean Hodograph (PH) spline within each corridor. The PH spline, unlike traditional geometric paths, extends free space dynamically associated with each corridor, supporting the precise computation of time-optimal paths.
3. Time Minimization Optimization: The final stage solves a spatial reformulation of the time-minimization problem. Here, the problem is spatially redefined using PH splines to align with system dynamics, yielding a globally time-optimal trajectory by exploring entire available free space.

Technical Contributions

The paper presents significant advancements in several areas:

• Spatial Reformulation and Singularity-Free Dynamic Modeling: Utilizing spatial reformulation, the paper shows that it is possible to map system dynamics spatially. This transformation aligns the coordinate system according to path parameters rather than time, eliminating traditional singularities experienced in Frenet-Serret frames.
• Closed-Form PH Spline Generation: The authors devised a computationally efficient method to generate PH splines in closed form without additional optimization phases. This approach significantly reduces computational requirements, promoting real-time applications.
• System Agnostic Application: The flexibility of the SCTOMP framework is evident in its compatibility with varying dynamic systems and environments, from planar environments for small-scale cars to three-dimensional scenarios involving quadrotors.

Experimental Validation and Implications

The effectiveness of SCTOMP is demonstrated in experimental setups involving a planar autonomous car and a spatial quadrotor. Results indicate consistent outcomes in terms of trajectory optimality, irrespective of spline path variations, thus validating the framework's robustness even in complex and cluttered environments. Performance comparisons against contemporary methods underscore SCTOMP's superior capability in achieving minimal trajectory time.

Conclusions and Future Work

SCTOMP introduces a robust framework that addresses inherent limitations within the motion planning landscape by integrating spatial dynamics and efficient path computation methodologies. Moving forward, the potential to refine the first-stage corridor definition could further enhance trajectory optimality, catering to applications across diverse autonomous systems. Furthermore, the modularity of each stage permits integration with other advanced techniques, paving the way for extensive future explorations in real-world applications.