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A Modular Framework for Motion Planning using Safe-by-Design Motion Primitives

Marijan Vukosavljev, Zachary Kroeze, Angela P. Schoellig, Mireille E. Broucke

TL;DR

This paper addresses scalable, safe motion planning for multi-robot systems by introducing a modular, hierarchical framework that decouples high-level planning from low-level control via motion primitives. Key ideas include discretizing the output space into boxes $Y^*$, encoding feasibility via the Output Transition System, Maneuver Automaton, and Product Automaton, and synthesizing a hybrid control strategy that guarantees reach-avoid safety. The authors provide concrete motion primitives for double-integrator dynamics, establish conditions ensuring correct-by-design behavior, and show that parallel composition preserves these properties for multi-robot systems. Experimental validation on quadrocopters demonstrates robustness and flexibility, with three policy-generation methods (NDD, A*, Greedy) offering a spectrum of quality and computational trade-offs. The approach enables plug-and-play integration of different low-level controllers and planning algorithms, supporting safe operation in known environments.

Abstract

We present a modular framework for solving a motion planning problem among a group of robots. The proposed framework utilizes a finite set of low level motion primitives to generate motions in a gridded workspace. The constraints on allowable sequences of motion primitives are formalized through a maneuver automaton. At the high level, a control policy determines which motion primitive is executed in each box of the gridded workspace. We state general conditions on motion primitives to obtain provably correct behavior so that a library of safe-by-design motion primitives can be designed. The overall framework yields a highly robust design by utilizing feedback strategies at both the low and high levels. We provide specific designs for motion primitives and control policies suitable for multi-robot motion planning; the modularity of our approach enables one to independently customize the designs of each of these components. Our approach is experimentally validated on a group of quadrocopters.

A Modular Framework for Motion Planning using Safe-by-Design Motion Primitives

TL;DR

This paper addresses scalable, safe motion planning for multi-robot systems by introducing a modular, hierarchical framework that decouples high-level planning from low-level control via motion primitives. Key ideas include discretizing the output space into boxes , encoding feasibility via the Output Transition System, Maneuver Automaton, and Product Automaton, and synthesizing a hybrid control strategy that guarantees reach-avoid safety. The authors provide concrete motion primitives for double-integrator dynamics, establish conditions ensuring correct-by-design behavior, and show that parallel composition preserves these properties for multi-robot systems. Experimental validation on quadrocopters demonstrates robustness and flexibility, with three policy-generation methods (NDD, A*, Greedy) offering a spectrum of quality and computational trade-offs. The approach enables plug-and-play integration of different low-level controllers and planning algorithms, supporting safe operation in known environments.

Abstract

We present a modular framework for solving a motion planning problem among a group of robots. The proposed framework utilizes a finite set of low level motion primitives to generate motions in a gridded workspace. The constraints on allowable sequences of motion primitives are formalized through a maneuver automaton. At the high level, a control policy determines which motion primitive is executed in each box of the gridded workspace. We state general conditions on motion primitives to obtain provably correct behavior so that a library of safe-by-design motion primitives can be designed. The overall framework yields a highly robust design by utilizing feedback strategies at both the low and high levels. We provide specific designs for motion primitives and control policies suitable for multi-robot motion planning; the modularity of our approach enables one to independently customize the designs of each of these components. Our approach is experimentally validated on a group of quadrocopters.

Paper Structure

This paper contains 26 sections, 8 theorems, 46 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Graph Search and Trajectory Planning
  4. Formal Methods
  5. Motion Primitives
  6. Problem Statement
  7. Modular Framework
  8. Output Transition System
  9. Maneuver Automaton
  10. Product Automaton
  11. High-Level Plan
  12. Main Results
  13. Parallel Composition of Motion Primitives
  14. Motion Primitives for Integrator Systems
  15. Quadrocopter Applications
  16. ...and 11 more sections

Key Result

Theorem 4.1

Consider $q \in Q_{\textsc{\tiny PA}} \setminus Q_{\textsc{\tiny PA}}^f$ and suppose $| \Sigma_{\textsc{\tiny PA}}(q) | > 0$. Then $V$ satisfies where $q' = (l',c(q,\sigma)) \in Q_{\textsc{\tiny PA}}$, $e = (q,\sigma,q') \in E_{\textsc{\tiny PA}}$, $\bar{q} = (\bar{l},\bar{m}) \in Q_{\textsc{\tiny PA}}$, and $\bar{e}=(q,\sigma,\bar{q}) \in E_{\textsc{\tiny PA}}$.

Figures (13)

  • Figure 1: Crazyflie quadrocopters navigate in a cluttered environment. Video results are available at http://tiny.cc/modular-3alg.
  • Figure 2: Our modular framework consists of five modules.
  • Figure 3: A two output ($p = 2$) example of a reach-avoid task. Shown on the left is the feasible space ${\mathcal{P}}$ consisting of 15 non-obstacle boxes (not red) and the goal region ${\mathcal{G}}$ (green). The output transition system (OTS), which abstracts the box regions and their neighbour connectivity, is shown on the right. Shown below, the possible offsets towards a neighbouring box are labelled using $\Sigma = \{-1,0,1\}^2$.
  • Figure 4: The maneuver automaton edges $E_{\textsc{\tiny MA}}$ for the double integrator dynamics with $p = 1$. There are three motion primitives: Hold ($\mathscr{H}$), Forward ($\mathscr{F}$), and Backward ($\mathscr{B}$).
  • Figure 5: The closed-loop vector fields in the $(x_1,x_2)$ position-velocity state space for the Hold, Forward, and Backward motion primitives.
  • ...and 8 more figures

Theorems & Definitions (32)

  • Definition 4.1
  • Remark 4.1
  • Definition 4.2
  • Example 4.1
  • Remark 4.2
  • Definition 4.3
  • Remark 4.3
  • Remark 4.4
  • Example 4.2
  • Theorem 4.1
  • ...and 22 more