Geometric Optimal Control for Locomotion of Biologically Inspired Robotic Systems

动物和它们类似的生物启发机器人的性能优于传统机器人（例如，汽车、飞机、船）在许多环境中和用于许多任务。 不幸的是，生物启发机器人的控制与传统机器人的控制不同，阻止了它们的采用。像传统机器人一样轻松控制生物启发的机器人将显著改变机器人领域。 主要的挑战是运动需要时变的周期性控制输入，称为步态，以实现运动。 步态的离散性及其随时间变化的结构意味着标准的控制策略不适用。 如果要广泛采用，这类机器人必须像传统机器人一样易于控制。 该奖项支持对数学框架的基础研究，这将导致更简单的公式来控制这些机器人。 更简单的公式将对社会有价值，因为生物启发的机器人被设想为在各种机器人应用领域具有很大的实际用途，例如搜索和救援，防御，监视和工厂完整性检查。此外，受生物启发的机器人受到年轻人和公众的欢迎。我们将利用这一吸引力，以增加和扩大参与工程和工程研究。生物启发的机器人系统是典型的非完整系统，需要随时间变化的控制输入，使基于最优控制的轨迹设计具有挑战性。 此外，这些系统依赖于可参数化的、随时间变化的控制输入（称为步态）来产生运动。步态是不相交的控制，因为应用一种步态排除了另一种步态的使用。 因此，不仅控制输入必须是时变的，而且可达性属性是步态相关的，并且对于某些导航目标可能需要切换控制模式。由于这些挑战，这些系统的轨迹生成和规划的框架的发展仍然是一个悬而未决的问题。 利用微分几何，几何力学和平均理论的概念，利用这些机器人系统的几何和时间对称性，减少最优控制配方将被导出。这些概念的多模式，多维控制系统的连接将划定解决切换，最优控制问题与多个步态策略的系统。为了生成最优控制求解器的初始轨迹估计，我们将专门设计一种kino-dynamic路径规划算法，以结合生物启发机器人系统的几何和多步态特性。

Animals, and their analogous biologically-inspired robots out-perform traditional robots (e.g., cars, planes, boats) in many environments and for many tasks. Unfortunately, control of biologically-inspired robots differs from that of traditional robots, preventing their adoption. Achieving control of biologically-inspired robots with the same ease as traditional robots would markedly transform the field of robotics. The main challenge is that locomotion requires time-varying periodic control inputs, known as gaits, to achieve movement. The discrete nature of the gaits and their time-varying structure means that standard control strategies do not apply. It is critical that this class of robots be as simple to control as traditional robots if widespread adoption is to occur. This award supports fundamental research into a mathematical framework that will lead to simpler formulations for control of these robots. The simpler formulation will be of value to society as biologically-inspired robots are envisioned to be of great practical use for a variety of robotic application domains, such as search and rescue, defense, surveillance, and plant integrity inspection. Furthermore, biologically-inspired robots are quite popular with youth and the public. We will capitalize on this appeal to increase and broaden participation in engineering and engineering research.Biologically-inspired robotic systems are typically nonholonomic systems that require time-varying control inputs, making optimal control-based design of trajectories challenging. Further, these systems rely on families of parametrizable, time-varying control inputs, called gaits, to generate movement. Gaits are disjoint controls, in that applying one gait precludes the use of another. Thus, not only must the control input be time-varying, but the reachability properties are gait-dependent and may require switches of control modes for some navigation goals. On account of these challenges, the development of a framework for trajectory generation and planning of these systems is still an open problem. Drawing on concepts from differential geometry, geometric mechanics, and averaging theory to exploit the geometric and temporal symmetries of these robotic systems, a reduced optimal control formulation will be derived. The connection of these concepts to multi-mode, multi-dimensional control systems will be delineated to resolve the switched, optimal control problem associated to systems with multiple gait strategies. To generate initial trajectory estimates for the optimal control solver, we will specialize a kino-dynamic path planning algorithm to incorporate the geometric and multi-gait properties of biologically-inspired robotic systems.