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Dynamic Modeling and MPC for Locomotion of Tendon-Driven Soft Quadruped

Saumya Karan, Neerav Maram, Suraj Borate, Madhu Vadali

Abstract

SLOT (Soft Legged Omnidirectional Tetrapod), a tendon-driven soft quadruped robot with 3D-printed TPU legs, is presented to study physics-informed modeling and control of compliant legged locomotion using only four actuators. Each leg is modeled as a deformable continuum using discrete Cosserat rod theory, enabling the capture of large bending deformations, distributed elasticity, tendon actuation, and ground contact interactions. A modular whole-body modeling framework is introduced, in which compliant leg dynamics are represented through physically consistent reaction forces applied to a rigid torso, providing a scalable interface between continuum soft limbs and rigid-body locomotion dynamics. This formulation allows efficient whole-body simulation and real-time control without sacrificing physical fidelity. The proposed model is embedded into a convex model predictive control framework that optimizes ground reaction forces over a 0.495 s prediction horizon and maps them to tendon actuation through a physics-informed force-angle relationship. The resulting controller achieves asymptotic stability under diverse perturbations. The framework is experimentally validated on a physical prototype during crawling and walking gaits, achieving high accuracy with less than 5 mm RMSE in center of mass trajectories. These results demonstrate a generalizable approach for integrating continuum soft legs into model-based locomotion control, advancing scalable and reusable modeling and control methods for soft quadruped robots.

Dynamic Modeling and MPC for Locomotion of Tendon-Driven Soft Quadruped

Abstract

SLOT (Soft Legged Omnidirectional Tetrapod), a tendon-driven soft quadruped robot with 3D-printed TPU legs, is presented to study physics-informed modeling and control of compliant legged locomotion using only four actuators. Each leg is modeled as a deformable continuum using discrete Cosserat rod theory, enabling the capture of large bending deformations, distributed elasticity, tendon actuation, and ground contact interactions. A modular whole-body modeling framework is introduced, in which compliant leg dynamics are represented through physically consistent reaction forces applied to a rigid torso, providing a scalable interface between continuum soft limbs and rigid-body locomotion dynamics. This formulation allows efficient whole-body simulation and real-time control without sacrificing physical fidelity. The proposed model is embedded into a convex model predictive control framework that optimizes ground reaction forces over a 0.495 s prediction horizon and maps them to tendon actuation through a physics-informed force-angle relationship. The resulting controller achieves asymptotic stability under diverse perturbations. The framework is experimentally validated on a physical prototype during crawling and walking gaits, achieving high accuracy with less than 5 mm RMSE in center of mass trajectories. These results demonstrate a generalizable approach for integrating continuum soft legs into model-based locomotion control, advancing scalable and reusable modeling and control methods for soft quadruped robots.
Paper Structure (33 sections, 21 equations, 13 figures, 4 tables, 1 algorithm)

This paper contains 33 sections, 21 equations, 13 figures, 4 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. SYSTEM OVERVIEW
  3. SINGLE LEG DYNAMIC MODEL
  4. Assumptions
  5. From Continuous to Discrete Cosserat Rod Formulation
  6. Model Calibration Procedure
  7. Force–Moment Balance and Numerical Simulation
  8. Internal Forces and Moments
  9. Tendon Tension
  10. Ground Contact and Friction
  11. Restoring Force to Initial Configuration
  12. Damping Force
  13. Cosserat Rod Dynamics Formulation
  14. Node-Level Dynamic Equations
  15. SLOT WHOLE-BODY MODELING
  16. ...and 18 more sections

Figures (13)

  • Figure 1: SLOT robot hardware
  • Figure 2: Single-leg deformation under tendon actuation.
  • Figure 3: Force application from four Cosserat rod legs onto the rigid cuboid torso.
  • Figure 4: Model Predictive Control block diagram.
  • Figure 5: Comparison of experimental and simulated vertical position $z(t)$ at four locations along the single leg—Node 0 (base), Node 10 (one-third length), Node 20 (two-thirds length), and Node 30 (tip).
  • ...and 8 more figures