Combining Optimization, Machine Learning, and Model Structure to Improve the Robustness and Agility of Modern Bipedal Machines

人们正在制造双足机器人来帮助搜索和救援，提供最后一英里的包裹递送，以及在家中为人们提供帮助。设计下肢外骨骼是为了帮助中风甚至严重受伤导致瘫痪的病人恢复行走能力。虽然让双足机器人行走和病人安全地操作下肢外骨骼所需的反馈控制算法并不相同，但它们有足够的共同点，因此将它们的研究结合起来是有见地和重要的。该项目将快速计算两足动力系统能量最优解的最新进展与机器学习数学和几何控制理论相结合，以实现两足行走的前所未有的性能和安全性。拟议的研究将极大地扩展机器人的类别，反馈控制器可以被设计成具有可证明的稳定性，它将大大提高安全性，而外骨骼可以让截瘫患者不使用拐杖行走。在这项研究中需要克服的众多技术挑战之一是描述这些有腿机器运动的数学模型的复杂性。例如，打印出这里研究的外骨骼的象征性模型需要数千页。如果有人打开这些文件来研究它们，它们将是不可理解的。然而，PI和他的学生为设计这些机器的反馈控制器提供了具体的方法，并深入探讨了闭环系统的行为方式。这就是反馈控制理论与现代计算工具结合的美妙之处。此外，每年，PI和他的学生通过向数百名从小学到高中的学生参观他的机器人实验室来分享工程的兴奋，分享STEM领域职业生涯的兴奋和个人成就感。主要大学的校长和公司的管理团队参观他的实验室，纯粹是为了看到一个机器人做一些令人惊奇的事情，但同时，几乎是普通的：大致像人一样走路。PI与媒体合作，与公众分享尖端工程研究的兴奋之情，以及它如何造福社会。该项目寻求在两足机器人和下肢外骨骼反馈控制器的理论概念和实际合成方面取得重大进展。该理论将在cassie系列两足机器人和外骨骼上进行仔细的测试。该提案的理论推力旨在减轻高维双足模型（30维或更多）所造成的障碍，而不是诉诸于机器人文献中太常见的简化钟摆模型。该研究旨在直接与机器人的完整模型一起工作，使其能够产生充分利用其功能的运动，同时尊重执行器的局限性，地面接触力和地形可变性。该过程从轨迹优化开始，设计高维模型的开环周期行走运动，然后在此解决方案中添加一组精心选择的模型的额外开环轨迹，以转向标称运动。监督式机器学习用于从开环行为（即输入和状态轨迹的集合）中提取低维状态变量实现（即低维流形和相关向量场）。利用双足机器人力学模型的特殊结构，将低维模型嵌入到原模型中，使其既具有不变性又具有局部指数吸引力，并证明了该模型在机器人的全状态空间中具有局部指数稳定性。周期轨道之间的过渡也将得到解决。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Bipedal robots are being built to aid in search and rescue, provide last mile delivery of packages, and to assist people in their homes. Lower-limb exoskeletons are being designed to help patients recover the ability to walk after strokes or even severe injuries resulting in paralysis. While the feedback control algorithms required to allow a bipedal robot to walk and a patient to safely operate a lower-limb exoskeleton are not identical, they share enough common elements that pursing their investigation in tandem is insightful and important. This project combines recent advances in the ability to quickly compute energy optimal solutions of bipedal dynamical systems with the mathematics of machine learning and geometric control theory to achieve unprecedented performance and safety in bipedal walking. The proposed research will greatly expand the class of robots for which feedback controllers can be designed with provable stability and it will significantly enhance the safety than can be achieved with exoskeletons that allow a paraplegic to walk without the use of crutches. One of the many technical challenges to be overcome in this research is the complexity of the mathematical models that describe the movement these legged machines. For example, printing out the symbolic model for the exoskeleton studied here would take thousands of pages. If a human ever opened the files to examine them, they would be incomprehensible. Yet, the PI and his students provide concrete means for designing feedback controllers for these machines and say deep things about how the closed-loop system will behave. This is the beauty of feedback control theory when it is married with modern computational tools. In addition, each year, the PI and his students share the excitement of engineering by giving tours of his robotics lab to hundreds of students, from grade school through high school, sharing the excitement and personal fulfillment of careers in STEM fields. Presidents of major universities and management teams of corporations visit his lab for the pure pleasure of seeing a robot doing something amazing and yet at the same time, almost ordinary: walking roughly like a human. The PI works with the media to share with the general public the excitement of cutting-edge engineering research and how it benefits society. The project seeks major advances in the theoretical conception and practical synthesis of feedback controllers for bipedal robots and lower-limb exoskeletons. The theory will be carefully tested on a Cassie-series bipedal robot and an exoskeleton. The theoretical thrust of the proposal aims to mitigate obstructions imposed by high-dimensional bipedal models (dimension 30 or more), without resorting to simplified pendulum models that are all too common in the robotics literature. The research seeks to work directly with the full model of the robot, making it possible to generate motions that exploit its full capabilities while respecting actuator limitations, ground contact forces, and terrain variability. The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model, and then adding to this solution, a carefully selected set of additional open-loop trajectories of the model that steer toward the nominal motion. Supervised Machine Learning is used to extract from the open-loop behavior (i.e., the collection of input and state trajectories) a low-dimensional state-variable realization (i.e., a low-dimensional manifold and associated vector field). The special structure of mechanical models of bipedal robots is used to embed the low-dimensional model in the original model in such a manner that it is both invariant and locally exponentially attractive, and show that this locally exponentially stabilizes the desired walking motion in the full state space of the robot. Transitions among periodic orbits will also be addressed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.