Geometric Optimal Control for Locomotion of Biologically Inspired Robotic Systems

在许多环境和许多任务中，动物和类似的受生物启发的机器人比传统机器人（如汽车、飞机、船只）表现得更好。不幸的是，受生物启发的机器人的控制与传统机器人不同，这阻碍了它们的采用。如果能像控制传统机器人一样轻松地控制仿生机器人，将极大地改变机器人领域。主要的挑战是，运动需要时变的周期性控制输入，即所谓的步态来实现运动。步态的离散性及其时变结构意味着标准控制策略不适用。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，这一点至关重要。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。更简单的配方将对社会有价值，因为受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，国防，监视和工厂完整性检查。此外，受生物启发的机器人很受年轻人和公众的欢迎。我们将利用这一呼吁来增加和扩大对工程和工程研究的参与。受生物启发的机器人系统是典型的非完整系统，需要时变控制输入，这使得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时变控制输入，称为步态，来产生运动。步态是脱节的控制，因为使用一种步态排除了另一种步态的使用。因此，不仅控制输入必须时变，而且可达性属性与步态相关，并且可能需要为某些导航目标切换控制模式。由于这些挑战，这些系统的轨迹生成和规划框架的开发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，推导出一个简化的最优控制公式。这些概念与多模式、多维控制系统的联系将被描述，以解决与多步态策略系统相关的切换、最优控制问题。为了生成最优控制解算器的初始轨迹估计，我们将专门研究一种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.