Real-Time Control-Constrained DDP for Underactuated Balancing of Legged Robots

Abstract:This paper presents a real-time control-constrained Differential Dynamic Programming (DDP) framework for underactuated legged robots. To address the limitation of classical DDP in handling control constraints, we propose an Accelerated Projected Gradient (APG)-based control-constrained DDP (ABC-DDP), which efficiently computes constrained solutions and identifies active sets without repeated Karush-Kuhn-Tucker (KKT) inversions. A virtual constraint is introduced to integrate control constraints within a feasibility-driven multiple-shooting framework, enabling stable optimization even from dynamically infeasible initializations. The proposed method supports real-time model predictive control (MPC) with short horizons under strong underactuation. Simulation results demonstrate static two-leg standing under external disturbances, along with diverse dynamic motions including slow catwalk, upright walking, and high-speed running within a unified MPC framework. To the best of our knowledge, this is the first demonstration of static two-leg standing of a quadruped robot achieved using real-time finite-horizon MPC.

Robotics (cs.RO); Optimization and Control (math.OC)

arXiv:2608.18552 [cs.RO]

(or arXiv:2608.18552v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2608.18552 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1109/LRA.2026.3723262 Focus to learn more DOI(s) linking to related resources

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