Galileo：一种用于腿式机器人的伪谱配点框架
Galileo: A Pseudospectral Collocation Framework for Legged Robots
AI总结：
本文提出Galileo框架，通过变量变换实现李群上的伪谱配点轨迹优化，并集成MPC与QP全身控制，在Go1和HURON机器人上验证了动态机动的可行性。
摘要：
腿式机器人的动态机动由于复杂的动力学和接触约束而面临困难挑战。本文介绍了一种用于连续时间多阶段问题的通用轨迹优化框架。我们提出了一种新的转录方案，使得伪谱配点能够直接在李群（如SE(3)和四元数）上进行优化，而无需特殊的归一化约束。关键见解在于变量变换——我们选择对切向量的历史进行优化，而非状态本身。我们的方法采用改进的勒让德-高斯-拉道（LGR）方法，为各种腿式机器人生成动态运动。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MPC输出。在Go1宇树和WPI HURON人形机器人上的结果证实了规划轨迹的可行性。
英文摘要：
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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