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.
Versions
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BibTeX
@misc{nam2026realtime,
title = {{Real-Time Control-Constrained DDP for Underactuated Balancing of Legged Robots}},
author = {SeongWon Nam and Hyunyong Lee and Hansol Kang and Jiman Park and Yeongwoo Son and Bumsu Yi and Jaeyoung Oh and Hyouk Ryeol Choi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.18552},
eprint = {2608.18552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18552},
}
RIS
TY - UNPB
TI - Real-Time Control-Constrained DDP for Underactuated Balancing of Legged Robots
AU - SeongWon Nam
AU - Hyunyong Lee
AU - Hansol Kang
AU - Jiman Park
AU - Yeongwoo Son
AU - Bumsu Yi
AU - Jaeyoung Oh
AU - Hyouk Ryeol Choi
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.18552
UR - https://arxiv.org/abs/2608.18552
AB - 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.
ER -