Locomotion on Constrained Footholds via Layered Architectures and Model Predictive Control

Computing stabilizing and optimal control actions for legged locomotion in real time is difficult due to the nonlinear, hybrid, and high dimensional nature of these robots. The hybrid nature of the system introduces a combination of discrete and continuous variables which causes issues for numerical optimal control. To address these challenges, we propose a layered architecture that separates the choice of discrete variables and a smooth Model Predictive Controller (MPC). The layered formulation allows for online flexibility and optimality without sacrificing real-time performance through a combination of gradient-free and gradient-based methods. The architecture leverages a sampling-based method for determining discrete variables, and a classical smooth MPC formulation using these fixed discrete variables. We demonstrate the results on a quadrupedal robot stepping over gaps and onto terrain with varying heights. In simulation, we demonstrate the controller on a humanoid robot for gap traversal. The layered approach is shown to be more optimal and reliable than common heuristic-based approaches and faster to compute than pure sampling methods.

@article{olkin2025_2506.09979,
  title={ Locomotion on Constrained Footholds via Layered Architectures and Model Predictive Control },
  author={ Zachary Olkin and Aaron D. Ames },
  journal={arXiv preprint arXiv:2506.09979},
  year={ 2025 }
}