用数学工具让四足机器人实时切换跑步、跳跃等步态
Koopman Operator Based Linear Model Predictive Control for 2D Quadruped Trotting, Bounding, and Gait Transition
- 用柯普曼算子构建高维线性模型，保留系统非线性特征
- 在平坦和崎岖地形上实现跑步、跳跃及步态切换的在线控制
- 适合研究机器人运动规划与自适应控制的学者参考
四足机器人的在线最优控制可使其在新环境中自主规划运动。线性模型预测控制（LMPC）因其在实时控制中的可行性而受到关注：在有限时间窗口内建立带二次代价和线性约束的优化问题，并即时求解。然而，LMPC依赖于对运动方程（EOM）的线性化，可能导致解的质量下降。本文采用柯普曼算子理论与扩展动态模态分解（EDMD），在高维空间中构建系统线性模型，从而保留EOM的非线性特性。分别使用不同线性模型描述空中阶段与地面接触阶段。结合LMPC，在水平与不平地形上成功演示了跑步、跳跃及从跳跃到跑步、跑步到跳跃的步态转换。主要创新在于利用柯普曼算子构建四足系统的混合线性模型，并实现多种步态及步态转换的在线生成。
原文摘要 · Abstract (English)
Online optimal control of quadrupedal robots would enable them to plan their movement in novel scenarios. Linear Model Predictive Control (LMPC) has emerged as a practical approach for real-time control. In LMPC, an optimization problem with a quadratic cost and linear constraints is formulated over a finite horizon and solved on the fly. However, LMPC relies on linearizing the equations of motion (EOM), which may lead to poor solution quality. In this paper, we use Koopman operator theory and the Extended Dynamic Mode Decomposition (EDMD) to create a linear model of the system in high dimensional space, thus retaining the nonlinearity of the EOM. We model the aerial phase and ground contact phases using different linear models. Then, using LMPC, we demonstrate bounding, trotting, and bound-to-trot and trot-to-bound gait transitions in level and rough terrains. The main novelty is the use of Koopman operator theory to create hybrid models of a quadrupedal system and demonstrate the online generation of multiple gaits and gaits transitions.
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