The problem of motion planning for affine control systems consists of designing control inputs that drive a system from a well-defined initial to final states in a desired amount of time. For control systems with drift, however, understanding which final states are reachable in a given time, or reciprocally the amount of time needed to reach a final state, is often the most difficult part of the problem. We address this issue in this paper and introduce a new method to solve motion planning problems for affine control systems, where the motion desired can have indefinite boundary conditions and the time required to perform the motion is free. The method extends on our earlier work on motion planning for systems without drift. A canonical example of parallel parking of a unicycle with constant linear velocity is provided in this paper to demonstrate our algorithm.

中文翻译：

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具有无限边界条件和自由终端时间的仿射控制系统的几何运动规划

仿射控制系统的运动规划问题包括设计控制输入，以在所需的时间内将系统从明确定义的初始状态驱动到最终状态。然而，对于具有漂移的控制系统，了解在给定时间内可以达到哪些最终状态，或者相反地了解达到最终状态所需的时间量，通常是问题中最困难的部分。我们在本文中解决了这个问题，并介绍了一种新方法来解决仿射控制系统的运动规划问题，其中所需的运动可以具有不确定的边界条件，并且执行运动所需的时间是免费的。该方法扩展了我们早期的无漂移系统运动规划工作。