提出实时控制约束的优化框架，让欠驱动四足机器人稳定站立和多种动态行走。
Real-Time Control-Constrained DDP for Underactuated Balancing of Legged Robots
- 用加速投影梯度法避免重复求解KKT条件，高效处理控制约束。
- 在强欠驱动下实现短时域模型预测控制，支持高速奔跑等复杂动作。
- 首次实现实时有限时域MPC下的四足机器人静态双足站立。
本文提出一种面向欠驱动腿式机器人的实时控制约束微分动态规划（DDP）框架。为解决经典DDP在处理控制约束时的局限性，提出基于加速投影梯度（APG）的控制约束DDP（ABC-DDP），无需重复求解Karush-Kuhn-Tucker（KKT）条件即可高效计算约束解并识别活跃集。引入虚拟约束，将控制约束融入以可行性为导向的多段射击框架，即使从动力学不可行的初始状态也能实现稳定优化。所提方法支持在强欠驱动条件下进行短时域模型预测控制（MPC）。仿真结果展示了在外部扰动下的静态双足站立，以及慢步行走、直立行走和高速奔跑等多种动态运动，均在统一MPC框架内实现。据我们所知，这是首个使用实时有限时域MPC实现四足机器人静态双足站立的案例。
原文摘要 · Abstract (English)
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.
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