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iDb-RRT: Sampling-based Kinodynamic Motion Planning with Motion Primitives and Trajectory Optimization

Joaquim Ortiz-Haro, Wolfgang Hönig, Valentin N. Hartmann, Marc Toussaint, Ludovic Righetti

TL;DR

iDb-RRT is a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework, which is probabilistically complete and can be implemented in forward or bidirectional mode.

Abstract

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.

iDb-RRT: Sampling-based Kinodynamic Motion Planning with Motion Primitives and Trajectory Optimization

TL;DR

iDb-RRT is a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework, which is probabilistically complete and can be implemented in forward or bidirectional mode.

Abstract

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.
Paper Structure (24 sections, 4 equations, 3 figures, 1 table, 4 algorithms)

This paper contains 24 sections, 4 equations, 3 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Definition
  4. iDb-RRT
  5. Background
  6. Overview
  7. Db-RRT: RRT with Motion Primitives
  8. Db-RRT-Connect and other Db-RRT variants
  9. Backward and Bidirectional Search
  10. Asymptotically Optimal Algorithms
  11. Trajectory Optimization
  12. Analysis
  13. Experiments
  14. Dynamical Systems
  15. Metrics
  16. ...and 9 more sections

Figures (3)

  • Figure 1: iDb-RRT combines a forward or bidirectional RRT search with motion primitives (Db-RRT) and trajectory optimization iteratively. (a,b) In the search step, the RRT is expanded by connecting motion primitives with a bounded discontinuity. (c) The output of the RRT is a trajectory with a bounded discontinuity in the dynamics constraints. (d) Using trajectory optimization, we generate a dynamically feasible trajectory. Problem visualization: Planar Rotor in Double bugtrap.
  • Figure 2: Top: Four motion primitives in the system Planar rotor. The initial state (green), final state (red) and duration are randomized. Bottom: During the search step (Db-RRT), motion primitives are connected allowing for a bounded discontinuity. In this visualization, we connect these four motion primitives from left to right. The green and red configurations indicate the first and last configurations of each primitive. Note that their rotation component does not match exactly (further, discontinuities in the velocity components are not shown).
  • Figure 3: Five kinodynamic motion planning problems in our benchmark Dynobench, with a solution found by iDb-RRT-C. (a) Rotor Pole - Up obstacles 2 (b) Unicycle 2 - Narrow passage (c) Car with Trailer - Double bugtrap (d) Quadrotor v0 - Recovery obstacles 2 (e) Quadrotor v1 - Double window.

Theorems & Definitions (2)

  • Definition 1: Discontinuity Bounded Solution
  • Definition 2: Motion Primitive