Designing Certified Controllers to Prevent Falls for Legged Robots

该项目将研究腿式机器人的控制器，尽管缺乏有关操作条件的完整信息，包括地形和机器人属性的不确定性，但仍能可靠地工作。这种方法与以前的方法不同，因为它的重点完全是保持平衡。有三个综合研究任务。首先是创建一个可行的算法来确定腿式机器人的起始位置，从该位置可以避免跌倒。第二个是预先计算一个所谓的“安全集”的控制输入，保证避免下降。这两项任务都将混合的非线性动力学嵌入到线性偏微分方程中，该方程从一组可接受的最终状态向后传播，以纳入不确定性的影响。第三个任务是使用可重构腿式机器人平台的结果的实验评估。作为第三项任务的一部分，人类操作员将被允许向腿式机器人发出任意命令。命令过滤器将修改用户输入，使其位于安全集内。因此，操作员将能够在机器人不摔倒的情况下发出任何命令。腿式机器人系统是搜索和救援任务或核电站维修或拆卸的理想候选人。然而，这种系统的成功远程操作是具有挑战性的。因此，有保证的安全操作将使这些系统成为一种可行的手段，使第一反应者免受伤害。研究中的技术可以扩展到机器人的其他领域，如主动假肢或外骨骼，从而使那些遭受丧失行动能力的人的生活受益。本项目将构建一种新的自动控制综合优化方案，以在存在模型不确定性的情况下为腿式机器人系统的安全性提供确定性保证。而不是依赖于线性化或假设任意控制的权威，在这个项目中考虑的方法将解决以下三个目标：首先，一个新的凸优化工具，有效地计算一组状态的腿机器人系统，具有小于用户指定的概率，避免福尔斯，尽管在连续和接触动态的不确定性。第二，一种新的控制合成工具，用于预先计算防止福尔斯下降的控制集合，以避免下降的状态集合。最后，一个交互式的现实世界的设置，其中用户可以应用任意输入的腿式机器人，然后修改，以确保在各种地形的安全操作;这种设置将验证强大的合成方法，同时允许建模者自信地探索配置的腿式机器人，很少被认为是迄今为止，由于现有的控制设计技术的限制。

This project will investigate controllers for legged robots that work reliably despite lacking full information about operating conditions, including uncertainty about terrain and robot properties. The approach differs from previous approaches in that the focus is entirely on maintaining balance. There are three integrated research tasks. First is creation of a feasible algorithm to determine starting positions of a legged robot from which falling can be avoided. Second is pre-computation of a so-called "safe set" of control inputs that is guaranteed to avoid falling. Both these tasks embed the hybrid, nonlinear dynamics of walking into a linear partial differential equation, which is propagated backwards in time from a set of acceptable final states to incorporate the effects of uncertainty. The third task is experimental evaluation of the results using a reconfigurable legged robot platform. As part of the third task, a human operator will be allowed to give arbitrary commands to a legged robot. A command filter will modify the user input so that it lies within the safe set. Thus the operator will be able to give any command without the robot falling. Legged robotic systems are an ideal candidate for search and rescue missions or nuclear power plant repair or disassembly. However successful teleoperation of such systems is challenging. Thus guaranteed safe operation will make these systems a viable means of keeping first responders out of harm's way. The techniques under study can be extended to other fields of robotics, such as active prostheses or exoskeletons, thereby benefitting the lives of those suffering from loss of mobility.This project will construct a novel optimization scheme for automated control synthesis to provide deterministic guarantees on the safety of a legged robotic system in the presence of model uncertainty. Rather than rely upon linearizations or assume arbitrary control authority, the approach considered in this project will address the following three aims: First, a new convex optimization tool to efficiently compute the set of states of a legged robotic system that have less than a user specified probability of avoiding falls in spite of uncertainty in the continuous and contact dynamics. Second, a novel control synthesis tool to pre-compute the set of controls that prevent falls for the set of states that can avoid falling. Finally, an interactive real-world setup wherein users can apply arbitrary inputs to a legged robot which are then modified to ensure safe operation across a variety of terrains; this setup will validate the robust synthesis method while allowing modelers to confidently explore configurations of a legged robot that have been rarely considered to date due to the limitations of existing control design techniques.