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Safe Legged Locomotion using Collision Cone Control Barrier Functions (C3BFs)

Manan Tayal, Shishir Kolathaya

TL;DR

The Quadratic Program (QP) formulation of C3 BF is introduced, referred to as C3BF-QP, which serves as a protective filter layer atop a reference controller to ensure the legged robots' safety during operation.

Abstract

Legged robots exhibit significant potential across diverse applications, including but not limited to hazardous environment search and rescue missions and the exploration of unexplored regions both on Earth and in outer space. However, the successful navigation of these robots in dynamic environments heavily hinges on the implementation of efficient collision avoidance techniques. In this research paper, we employ Collision Cone Control Barrier Functions (C3BF) to ensure the secure movement of legged robots within environments featuring a wide array of static and dynamic obstacles. We introduce the Quadratic Program (QP) formulation of C3BF, referred to as C3BF-QP, which serves as a protective filter layer atop a reference controller to ensure the robots' safety during operation. The effectiveness of this approach is illustrated through simulations conducted on PyBullet.

Safe Legged Locomotion using Collision Cone Control Barrier Functions (C3BFs)

TL;DR

The Quadratic Program (QP) formulation of C3 BF is introduced, referred to as C3BF-QP, which serves as a protective filter layer atop a reference controller to ensure the legged robots' safety during operation.

Abstract

Legged robots exhibit significant potential across diverse applications, including but not limited to hazardous environment search and rescue missions and the exploration of unexplored regions both on Earth and in outer space. However, the successful navigation of these robots in dynamic environments heavily hinges on the implementation of efficient collision avoidance techniques. In this research paper, we employ Collision Cone Control Barrier Functions (C3BF) to ensure the secure movement of legged robots within environments featuring a wide array of static and dynamic obstacles. We introduce the Quadratic Program (QP) formulation of C3BF, referred to as C3BF-QP, which serves as a protective filter layer atop a reference controller to ensure the robots' safety during operation. The effectiveness of this approach is illustrated through simulations conducted on PyBullet.
Paper Structure (11 sections, 2 theorems, 16 equations, 5 figures)

This paper contains 11 sections, 2 theorems, 16 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Organisation
  3. Preliminaries
  4. Control barrier functions (CBFs)
  5. Safety Filter Design
  6. Collision Cone CBF (C3BF) candidate
  7. Collision Cone CBFs on Legged Robots
  8. Collision Avoidance - Vertical Obstacles
  9. Collision Avoidance - Horizontal Obstacles
  10. Simulation Results
  11. Conclusions

Key Result

Theorem 1

Given the above model, the proposed CBF candidate eqn:CC-CBF-ver with $p_{\rm{rel}},v_{\rm{rel}}$ defined by eq:pos_ver, eq:vel_ver is a valid CBF defined for the set $\mathcal{D}$.

Figures (5)

  • Figure 1: Quadruped (left) and Bipedal (right) Legged Robots
  • Figure 2: Construction of collision cone for an elliptical obstacle considering the ego-vehicle's dimensions (width: $w$).
  • Figure 3: Interaction with static obstacles in (a) Quadruped and in (b) Biped Robots
  • Figure 4: Interaction with moving obstacles in (a) Quadruped and in (b) Biped Robots
  • Figure 5: Interaction with horizontal obstacle in Quadruped Robot

Theorems & Definitions (5)

  • Definition 1: Control barrier function (CBF)
  • Theorem 1
  • proof
  • Theorem 2
  • proof