Abstract We address in this paper the problem of planning motion of free floating robot with state constraints. Due to the conservation of angular and linear momentum during the in-air motion, the problem is two-fold: one needs to design, in addition to the in-air motion, the initial impulse that imparts the robot with the appropriate momentum to perform a desired motion. The existence of state constraints such as joint limit makes the planning problem even more challenging. We propose in this paper a new method to address this problem. The method is a homotopy method which deforms an arbitrary path connecting the desired initial and final states to a feasible trajectory between these states, that is a trajectory that meets the system’s dynamics and constraints. From this trajectory, the method extracts both the controls and initial momentum needed to perform the motion. The deformation of path is leaded by geometric heat flow which is defined by a Riemannian metric that encodes the system dynamics and state constraints. We illustrate the method by designing somersault motions for a diver robot.

中文翻译：

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基于状态约束的热流法机器人空中运动规划

摘要 本文解决了具有状态约束的自由浮动机器人的运动规划问题。由于在空中运动过程中角动量和线动量守恒，问题有两方面：一是除了空中运动之外，还需要设计初始冲量，赋予机器人适当的动量以执行想要的运动。联合极限等状态约束的存在使得规划问题更具挑战性。我们在本文中提出了一种新方法来解决这个问题。该方法是一种同伦方法，它将连接所需初始和最终状态的任意路径变形为这些状态之间的可行轨迹，即满足系统动力学和约束的轨迹。从这个轨迹来看，该方法提取了执行运动所需的控制和初始动量。路径的变形由几何热流引导，几何热流由编码系统动力学和状态约束的黎曼度量定义。我们通过为潜水机器人设计翻筋斗运动来说明该方法。