Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM for control captures critical task-relevant aspects of the full dynamics while remaining low dimensional. However, planning within the reduced-order space unavoidably constrains the full model, and hence we sacrifice the full potential of the robot. In the community of legged locomotion, this has lead to a search for better model extensions, but many of these extensions require human intuition, and there has not existed a principled way of evaluating the model performance and discovering new models. In this work, we propose a model optimization algorithm that automatically synthesizes reduced-order models, optimal with respect to a user-specified distribution of tasks and corresponding cost functions. To demonstrate our work, we optimized models for a bipedal robot Cassie. We show in simulation that the optimal ROM reduces the cost of Cassie's joint torques by up to 23% and increases its walking speed by up to 54%. We also show hardware result that the real robot walks on flat ground with 10% lower torque cost. All videos and code can be found at https://sites.google.com/view/ymchen/research/optimal-rom.

翻译：简化模型（ROM）因其简洁性在在线运动规划中广泛应用。一个好的控制ROM应在保持低维度的同时，捕捉完整动力学中与任务相关的关键特征。然而，在简化空间中规划不可避免地限制了完整模型，因而牺牲了机器人的全部潜力。在腿部运动控制领域，这促使研究者探索更好的模型扩展，但许多扩展依赖于人类直觉，且缺乏评估模型性能及发现新模型的系统性方法。本文提出一种模型优化算法，可针对用户指定的任务分布及相应代价函数自动合成最优简化模型。为验证该算法，我们针对双足机器人Cassie优化了模型。仿真结果表明，最优ROM使Cassie关节扭矩代价降低达23%，行走速度提升达54%。硬件实验也证实，真实机器人在平地上行走时扭矩代价降低10%。所有视频与代码均可在https://sites.google.com/view/ymchen/research/optimal-rom 获取。