# MPC for Humanoid Gait Generation: Stability and Feasibility

arXiv: https://arxiv.org/abs/1901.08505 · HTML: https://mlsanity.com/paper/1901.08505/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Learning Humanoid Locomotion with World Model Reconstruction](https://mlsanity.com/paper/2502.16230/) (2025)
- [Hiking in the Wild: A Scalable Perceptive Parkour Framework for Humanoids](https://mlsanity.com/paper/2601.07718/) (2026)
- [CACTO: Continuous Actor-Critic with Trajectory Optimization -- Towards global optimality](https://mlsanity.com/paper/2211.06625/) (2022)
- [FRASA: An End-to-End Reinforcement Learning Agent for Fall Recovery and Stand Up of Humanoid Robots](https://mlsanity.com/paper/2410.08655/) (2024)
- [The Duke Humanoid: Design and Control For Energy Efficient Bipedal Locomotion Using Passive Dynamics](https://mlsanity.com/paper/2409.19795/) (2024)
- [CoRe-MoE: Contrastive Reweighted Mixture of Experts for Multi-Terrain Humanoid Locomotion with Gait Adaptation](https://mlsanity.com/paper/2606.04718/) (2026)

## Abstract (arXiv)

We present IS-MPC, an intrinsically stable MPC framework for humanoid gait generation which incorporates an explicit stability constraint in the formulation. The proposed method uses as prediction model a dynamically extended LIP where ZMP velocities are the control inputs, producing in real time a gait (including footsteps with the associated timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links the future ZMP velocities to the current system state so as to guarantee the essential requirement that the generated CoM trajectory is bounded with respect to the ZMP trajectory. Since the control horizon of the MPC algorithm is finite, only part of the future ZMP velocities are decision variables of the QP problem; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several possible options for the tail are discussed, and each of them is shown to correspond to a specific terminal constraint. A theoretical analysis of the feasibility of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, it is proved that IS-MPC guarantees stability of the CoM/ZMP dynamics if it is recursively feasible. Simulation and experimental results on the NAO and the HRP-4 humanoids are presented to illustrate the performance of the proposed method.