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KCFRC: Kinematic Collision-Aware Foothold Reachability Criteria for Legged Locomotion

Lei Ye, Haibo Gao, Huaiguang Yang, Peng Xu, Haoyu Wang, Tie Liu, Junqi Shan, Zongquan Deng, Liang Ding

TL;DR

The KCFRC algorithm is developed, which enables robots to validate foothold reachability in real time and can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.

Abstract

Legged robots face significant challenges in navigating complex environments, as they require precise real-time decisions for foothold selection and contact planning. While existing research has explored methods to select footholds based on terrain geometry or kinematics, a critical gap remains: few existing methods efficiently validate the existence of a non-collision swing trajectory. This paper addresses this gap by introducing KCFRC, a novel approach for efficient foothold reachability analysis. We first formally define the foothold reachability problem and establish a sufficient condition for foothold reachability. Based on this condition, we develop the KCFRC algorithm, which enables robots to validate foothold reachability in real time. Our experimental results demonstrate that KCFRC achieves remarkable time efficiency, completing foothold reachability checks for a single leg across 900 potential footholds in an average of 2 ms. Furthermore, we show that KCFRC can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.

KCFRC: Kinematic Collision-Aware Foothold Reachability Criteria for Legged Locomotion

TL;DR

The KCFRC algorithm is developed, which enables robots to validate foothold reachability in real time and can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.

Abstract

Legged robots face significant challenges in navigating complex environments, as they require precise real-time decisions for foothold selection and contact planning. While existing research has explored methods to select footholds based on terrain geometry or kinematics, a critical gap remains: few existing methods efficiently validate the existence of a non-collision swing trajectory. This paper addresses this gap by introducing KCFRC, a novel approach for efficient foothold reachability analysis. We first formally define the foothold reachability problem and establish a sufficient condition for foothold reachability. Based on this condition, we develop the KCFRC algorithm, which enables robots to validate foothold reachability in real time. Our experimental results demonstrate that KCFRC achieves remarkable time efficiency, completing foothold reachability checks for a single leg across 900 potential footholds in an average of 2 ms. Furthermore, we show that KCFRC can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.
Paper Structure (34 sections, 3 theorems, 8 equations, 17 figures, 4 tables, 2 algorithms)

This paper contains 34 sections, 3 theorems, 8 equations, 17 figures, 4 tables, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. Reachability in Robotics
  4. Foothold Reachability from Terrain Perspective
  5. Foothold Reachability from Kinematics Perspective
  6. Foothold Reachability Check through Trajectory Planner
  7. Overview of the Work
  8. Foothold Reachability Problem
  9. Problem Formulation and Simplification Assumption
  10. Sufficient Condition for Foothold Reachability
  11. Kinematic Collision-Aware FRC
  12. Terrain Representation
  13. Kinematics and Collision Detection
  14. Feasible Domain
  15. Guiding Surface Design
  16. ...and 19 more sections

Key Result

Lemma 1

For Problem prob:reachability, if $D_f \setminus D_o$ is homeomorphic to $D_f$, then there exists a path $f: [0, 1] \to (D_f \setminus D_o)$ such that $p = f(0)$ and $q = f(1)$.

Figures (17)

  • Figure 1: Kinematic Collision-Aware Foothold Reachability Criteria demonstration in barrier traversal. Blue cubes show validated reachable footholds, orange/red curves show initialized/optimized swing trajectories. The hexapod robot must carefully select footholds to navigate through the confined space. More supplemental materials are available at https://masteryip.github.io/fltplanner.github.io/ .
  • Figure 2: Foothold Evaluation Criteria. (a) Foot Collision checking for foot-terrain interference, (b) Kinematic Feasibility ensuring joint limits compliance, and (c) Leg Collision detecting segment-obstacle interference. These criteria require explicit trajectory generation for validation.
  • Figure 3: Reachability of the expected foothold. The foothold is reachable if feasible domain is not split by obstacles, and vice versa.
  • Figure 4: Overview of KCFRC. (a) Problem setup. (b) Feasible domain definition [Section \ref{['section:feasible_domain']}]. (c) Guiding surface generation [Section \ref{['section:guid_surf']}]. (d) Intersection border computing [Section \ref{['section:intersect_border']}]. (e) Reachability check [Section \ref{['section:reachability_check']}].
  • Figure 5: Diagram of the Sufficient Condition for Reachability (Theorem \ref{['theorem:reachability2']}).
  • ...and 12 more figures

Theorems & Definitions (10)

  • Definition 1: Foothold Reachability
  • Remark 1
  • Lemma 1
  • Definition 2: Guiding Surface $S_g$
  • Lemma 2: Existence of Guiding Surface
  • proof
  • Remark 2
  • Definition 3: Auxiliary Surface $S_a$
  • Theorem 1: Sufficient Condition for Reachability
  • proof