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Multi-layer Motion Planning with Kinodynamic and Spatio-Temporal Constraints

Jeel Chatrola, Abhiroop Ajith, Kevin Leahy, Constantinos Chamzas

TL;DR

The paper tackles motion planning under both kinodynamic and spatiotemporal constraints by proposing a novel three-layer framework that first reasons about region sequences, then generates a geometric lead path, and finally optimizes a kinodynamic trajectory using an STL-robustness cost without requiring steering functions. The approach leverages a Stable Sparse Tree (SST) foundation augmented with biased sampling around a guided geometric path, layer-based decomposition, and a propagation radius to maintain focus on spatial regions critical to satisfying the specification. A new, efficient STL encoding and a recursive robustness-based cost enable scalable optimization for complex temporal goals, including multi-goal sequencing and crossovers. Experimental results on a velocity-controlled Ackermann-car model demonstrate significant performance gains over baselines and the ability to produce sophisticated maneuvers that prior methods could not demonstrate, highlighting practical impact for time-constrained, nonholonomic planning tasks.

Abstract

We propose a novel, multi-layered planning approach for computing paths that satisfy both kinodynamic and spatiotemporal constraints. Our three-part framework first establishes potential sequences to meet spatial constraints, using them to calculate a geometric lead path. This path then guides an asymptotically optimal sampling-based kinodynamic planner, which minimizes an STL-robustness cost to jointly satisfy spatiotemporal and kinodynamic constraints. In our experiments, we test our method with a velocity-controlled Ackerman-car model and demonstrate significant efficiency gains compared to prior art. Additionally, our method is able to generate complex path maneuvers, such as crossovers, something that previous methods had not demonstrated.

Multi-layer Motion Planning with Kinodynamic and Spatio-Temporal Constraints

TL;DR

The paper tackles motion planning under both kinodynamic and spatiotemporal constraints by proposing a novel three-layer framework that first reasons about region sequences, then generates a geometric lead path, and finally optimizes a kinodynamic trajectory using an STL-robustness cost without requiring steering functions. The approach leverages a Stable Sparse Tree (SST) foundation augmented with biased sampling around a guided geometric path, layer-based decomposition, and a propagation radius to maintain focus on spatial regions critical to satisfying the specification. A new, efficient STL encoding and a recursive robustness-based cost enable scalable optimization for complex temporal goals, including multi-goal sequencing and crossovers. Experimental results on a velocity-controlled Ackermann-car model demonstrate significant performance gains over baselines and the ability to produce sophisticated maneuvers that prior methods could not demonstrate, highlighting practical impact for time-constrained, nonholonomic planning tasks.

Abstract

We propose a novel, multi-layered planning approach for computing paths that satisfy both kinodynamic and spatiotemporal constraints. Our three-part framework first establishes potential sequences to meet spatial constraints, using them to calculate a geometric lead path. This path then guides an asymptotically optimal sampling-based kinodynamic planner, which minimizes an STL-robustness cost to jointly satisfy spatiotemporal and kinodynamic constraints. In our experiments, we test our method with a velocity-controlled Ackerman-car model and demonstrate significant efficiency gains compared to prior art. Additionally, our method is able to generate complex path maneuvers, such as crossovers, something that previous methods had not demonstrated.

Paper Structure

This paper contains 16 sections, 9 equations, 4 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Problem Statement
  5. Kinodynamic Constraints
  6. Mission Specification
  7. Proposed Approach
  8. Discrete Region Orders
  9. Continuous Spatial Path
  10. Kinodynamic Spatial Temporal Path
  11. Biased Sampling
  12. Layer Assignment
  13. Propagation Radius
  14. Satisfy the Temporal constraints (Cost Function)
  15. Case Studies
  16. ...and 1 more sections

Figures (4)

  • Figure 1: A delivery robot tasked with reaching different regions in a time sensitive-manner.
  • Figure 2: Layer Assignment and connection of nodes, the magnified image shows the node that are rejected.
  • Figure 3: The figure shows rejection of nodes that deviate more than allowed by the propagation radius
  • Figure 4: Comparison of the SST-STL and LG-SST-STL planners across three experiments. The middle row displays the average best cost achieved by each planner over time. The bottom row compares the number of states in the graph.