直接在李群上优化腿式机器人轨迹，避免复杂约束。
Galileo: A Pseudospectral Collocation Framework for Legged Robots
- 用切向量历史代替状态变量，实现李群直接优化
- 基于修正LGR方法生成多阶段动态运动轨迹
- 在Go1和HURON上验证可行性，适合高速动态任务
腿式机器人的动态机动因复杂的动力学和接触约束而极具挑战。本文提出一种适用于连续时间多阶段问题的通用轨迹优化框架。引入一种新型转录方案，使伪谱配置可直接在李群（如SE(3)和四元数）上进行优化，无需特殊归一化约束。关键洞察在于变量变换——优化对象从状态本身改为切向量的历史。该方法采用修正的Legendre-Gauss-Radau（LGR）法生成多种腿式机器人的动态运动。我们将该方法实现为模型预测控制器（MPC），并使用基于二次规划（QP）的全身控制器跟踪其输出。在Go1 Unitree和WPI HURON人形机器人上的实验结果证实了所规划轨迹的可行性。
原文摘要 · Abstract (English)
Dynamic maneuvers for legged robots present a difficult challenge due to the complex dynamics and contact constraints. This paper introduces a versatile trajectory optimization framework for continuous-time multi-phase problems. We introduce a new transcription scheme that enables pseudospectral collocation to optimize directly on Lie Groups, such as SE(3) and quaternions without special normalization constraints. The key insight is the change of variables - we choose to optimize over the history of the tangent vectors rather than the states themselves. Our approach uses a modified Legendre-Gauss-Radau (LGR) method to produce dynamic motions for various legged robots. We implement our approach as a Model Predictive Controller (MPC) and track the MPC output using a Quadratic Program (QP) based whole-body controller. Results on the Go1 Unitree and WPI HURON humanoid confirm the feasibility of the planned trajectories.
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