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Torque-Minimizing Control Allocation for Overactuated Quadrupedal Locomotion

Mads Erlend Bøe Lysø, Esten Ingar Grøtli, Kristin Ytterstad Pettersen

TL;DR

This work addresses torque-efficient control of overactuated quadrupedal locomotion using a full-order model. It extends an offline nonlinear optimal control framework by enabling true overactuated input-output linearization through a least-squares control-allocation scheme, implemented with a pseudoinverse when the number of inputs exceeds outputs and preserving exponential orbital stability. The approach yields equal or lower torque expenditure without altering the target output trajectories, demonstrated in simulation on the ASTRo robot with notable reductions in torque and energy consumption. This method offers robust torque allocation during multi-contact gait phases, potentially improving energy efficiency in dynamic legged locomotion without sacrificing stability.

Abstract

In this paper, we improve upon a method for optimal control of quadrupedal robots which utilizes a full-order model of the system. The original method utilizes offline nonlinear optimal control to synthesize a control scheme which exponentially orbitally stabilizes the closed-loop system. However, it is not able to handle the overactuated phases which frequently occur during quadrupedal locomotion as a result of the multi-contact nature of the system. We propose a modified method, which handles overactuated gait phases in a way that utilizes the full range of available actuators to minimize torque expenditure without requiring output trajectories to be modified. It is shown that the system under the proposed controller exhibits the same properties, i.e. exponential orbital stability, with the same or lower point-wise torque magnitude. A simulation study demonstrates that the reduction in torque may in certain cases be substantial.

Torque-Minimizing Control Allocation for Overactuated Quadrupedal Locomotion

TL;DR

This work addresses torque-efficient control of overactuated quadrupedal locomotion using a full-order model. It extends an offline nonlinear optimal control framework by enabling true overactuated input-output linearization through a least-squares control-allocation scheme, implemented with a pseudoinverse when the number of inputs exceeds outputs and preserving exponential orbital stability. The approach yields equal or lower torque expenditure without altering the target output trajectories, demonstrated in simulation on the ASTRo robot with notable reductions in torque and energy consumption. This method offers robust torque allocation during multi-contact gait phases, potentially improving energy efficiency in dynamic legged locomotion without sacrificing stability.

Abstract

In this paper, we improve upon a method for optimal control of quadrupedal robots which utilizes a full-order model of the system. The original method utilizes offline nonlinear optimal control to synthesize a control scheme which exponentially orbitally stabilizes the closed-loop system. However, it is not able to handle the overactuated phases which frequently occur during quadrupedal locomotion as a result of the multi-contact nature of the system. We propose a modified method, which handles overactuated gait phases in a way that utilizes the full range of available actuators to minimize torque expenditure without requiring output trajectories to be modified. It is shown that the system under the proposed controller exhibits the same properties, i.e. exponential orbital stability, with the same or lower point-wise torque magnitude. A simulation study demonstrates that the reduction in torque may in certain cases be substantial.
Paper Structure (13 sections, 11 equations, 5 figures, 1 table)

This paper contains 13 sections, 11 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. System modeling
  3. Hybrid Dynamical System Formulation
  4. Continuous dynamics and constraints
  5. Discrete dynamics and transitions
  6. Guards and admissible domain
  7. Methods
  8. Offline optimal control
  9. IO-linearization and zero-dynamics
  10. Exponential Orbital Stabilization of full state
  11. Over-actuated input-output linearization
  12. Results
  13. Conclusions and future work

Figures (5)

  • Figure 1: Photo of the sprawling quadrupedal robot ASTRo
  • Figure 2: Phase portraits for base of optimized and simulated ambling gait. Red dots signify initial values.
  • Figure 3: Phase portraits for joints of optimized and simulated ambling gait. Red dots signify initial values.
  • Figure 4: Diagram for one cycle of an ambling gait.
  • Figure 5: Plots of absolute value of torques for left leg actuators for two consecutive gait cycles.