Control of Humanoid Robots with Parallel Mechanisms Using Differential Actuation Models
Victor Lutz, Ludovic De Matteïs, Virgile BATTO, Nicolas Mansard
AI summary
Problem
Modern humanoid robots use parallel actuator mechanisms to reduce leg inertia, but their non-linear transmission and loop-closure constraints make accurate modeling computationally expensive, forcing controllers to rely on simplified constant-ratio approximations that limit dynamic performance.
Approach
The authors derive a compact analytical formulation for standard four-bar and intricate four-bar transmissions, providing efficient first- and second-order derivatives for dynamics and an exact method to transfer serial-space impedance gains to the motor-space.
Key results
- Compact analytical model for four-bar and intricate four-bar transmissions
- Efficient first- and second-order derivatives for trajectory optimization and RL
- Analytical derivation of apparent transmission impedance for gain transfer
- Hardware validation on Bipetto robot showing improved accuracy and robustness
Why it matters
Provides a practical, low-cost method to incorporate exact parallel actuation dynamics into modern control and learning pipelines for next-generation humanoids.
Abstract
Several recently released humanoid robots, in- spired by the mechanical design of Cassie, employ actuator configurations in which the motors are displaced from the joints to reduce leg inertia. While studies accounting for the full kinematic complexity have demonstrated the benefits of these designs, the associated loop-closure constraints greatly increase computational cost and limit their use in control and learning. As a result, the non-linear transmission is often approximated by a constant reduction ratio, preventing exploitation of the mechanism’s full capabilities. This paper introduces a compact analytical formulation for the two standard knee and ankle mechanisms that captures the exact non-linear transmission while remaining computationally efficient. The model is fully differentiable up to second order with a minimal formulation, enabling low-cost evaluation of dynamic derivatives for trajec- tory optimization and of the apparent transmission impedance for reinforcement learning. We integrate this formulation into trajectory optimization and locomotion policy learning, and compare it against simplified constant-ratio approaches. Hardware experiments demonstrate improved accuracy and robustness, showing that the proposed method provides a practical means to incorporate parallel actuation into modern control algorithms.