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Optimal Gait Design for a Soft Quadruped Robot via Multi-fidelity Bayesian Optimization

Kaige Tan, Xuezhi Niu, Qinglei Ji, Lei Feng, Martin Törngren

TL;DR

This work tackles gait optimization for a tendon-driven soft quadruped by learning a parametric Hopf-CPG-based gait pattern and optimizing it with multi-fidelity Bayesian optimization to bridge the reality gap between simulation and real hardware. By coupling a GP-based BO, MTGP-based MFBO across fidelity levels, and an edge-computing architecture, the approach enables efficient sim-to-real adaptation and online refinement of gait parameters, reducing data and time requirements. The key contributions include a parametric gait generator tied to inverse kinematics, a MFBO framework for sim-to-real transfer, and an edge-enabled architecture that sustains real-time control. The results demonstrate substantial performance gains in physical deployment (e.g., MFBO achieving up to a 52.7% improvement over baselines) and effective bandwidth/latency benefits from edge off-loading, highlighting practical impact for soft-robotic locomotion in real-world settings.

Abstract

This study focuses on the locomotion capability improvement in a tendon-driven soft quadruped robot through an online adaptive learning approach. Leveraging the inverse kinematics model of the soft quadruped robot, we employ a central pattern generator to design a parametric gait pattern, and use Bayesian optimization (BO) to find the optimal parameters. Further, to address the challenges of modeling discrepancies, we implement a multi-fidelity BO approach, combining data from both simulation and physical experiments throughout training and optimization. This strategy enables the adaptive refinement of the gait pattern and ensures a smooth transition from simulation to real-world deployment for the controller. Moreover, we integrate a computational task off-loading architecture by edge computing, which reduces the onboard computational and memory overhead, to improve real-time control performance and facilitate an effective online learning process. The proposed approach successfully achieves optimal walking gait design for physical deployment with high efficiency, effectively addressing challenges related to the reality gap in soft robotics.

Optimal Gait Design for a Soft Quadruped Robot via Multi-fidelity Bayesian Optimization

TL;DR

This work tackles gait optimization for a tendon-driven soft quadruped by learning a parametric Hopf-CPG-based gait pattern and optimizing it with multi-fidelity Bayesian optimization to bridge the reality gap between simulation and real hardware. By coupling a GP-based BO, MTGP-based MFBO across fidelity levels, and an edge-computing architecture, the approach enables efficient sim-to-real adaptation and online refinement of gait parameters, reducing data and time requirements. The key contributions include a parametric gait generator tied to inverse kinematics, a MFBO framework for sim-to-real transfer, and an edge-enabled architecture that sustains real-time control. The results demonstrate substantial performance gains in physical deployment (e.g., MFBO achieving up to a 52.7% improvement over baselines) and effective bandwidth/latency benefits from edge off-loading, highlighting practical impact for soft-robotic locomotion in real-world settings.

Abstract

This study focuses on the locomotion capability improvement in a tendon-driven soft quadruped robot through an online adaptive learning approach. Leveraging the inverse kinematics model of the soft quadruped robot, we employ a central pattern generator to design a parametric gait pattern, and use Bayesian optimization (BO) to find the optimal parameters. Further, to address the challenges of modeling discrepancies, we implement a multi-fidelity BO approach, combining data from both simulation and physical experiments throughout training and optimization. This strategy enables the adaptive refinement of the gait pattern and ensures a smooth transition from simulation to real-world deployment for the controller. Moreover, we integrate a computational task off-loading architecture by edge computing, which reduces the onboard computational and memory overhead, to improve real-time control performance and facilitate an effective online learning process. The proposed approach successfully achieves optimal walking gait design for physical deployment with high efficiency, effectively addressing challenges related to the reality gap in soft robotics.
Paper Structure (21 sections, 20 equations, 10 figures, 3 tables, 1 algorithm)

This paper contains 21 sections, 20 equations, 10 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Gaussian Processes Model
  4. Bayesian Optimization
  5. Hopf Oscillator
  6. Parametric Gait Pattern Model
  7. Inverse Kinematics: Task Level to Motor Level
  8. Gait Pattern Generation
  9. Optimization Problem Formulation
  10. Adaptive Optimal Gait Design by Multi-fidelity Bayesian Optimization
  11. Reality Gap from the Digital Replica
  12. Multi-fidelity Bayesian Optimization
  13. System Architecture Overview
  14. Results and Validation
  15. Baseline Selection
  16. ...and 6 more sections

Figures (10)

  • Figure 1: Overview of the soft robot and its Tendon-driven Soft Actuator (TSA): (a) Rendered robot with key states. (b) Structure of TSA: rigid upper thigh and bendable lower section with $\alpha_b$. (c) Top view of bent TSA with $\alpha_r$. (d) TSA compression via equal tendon pull with $z_\textrm{l}$.
  • Figure 2: The non-harmonic oscillator response with varying frequencies. In this example, the initial state is randomized, and $[A,f,\alpha,\tau,k,\epsilon,\Delta t']\!=\![1,1.33,0.75,1,1000,5,0.25].$
  • Figure 3: Control system architecture. The actuator and electrical firmware are physically integrated into the robot. The unidirectional arrows surrounding radio waves denote the transmission and reception of messages between soft robots and the edge server.
  • Figure 4: BO training on simulation platform
  • Figure 5: MFBO physical training
  • ...and 5 more figures

Theorems & Definitions (1)

  • Remark 1