论文标题
动力学控制系统和间隙中的不连续性
Kinodynamic control systems and discontinuities in clearance
论文作者
论文摘要
我们研究了具有一般，封闭障碍物（或目标）的非线性控制系统的间隙（或最短时间）功能中不连续性的结构。我们就可以接受的轨迹与清除不连续性之间的相互作用建立了一般的结果：例如通过不连续性，瞬时会增加间隙，并沿最佳轨迹繁殖不连续性。然后，研究不连续性的足够条件，我们探索了一个速度的共同方向性条件，其特征是最小的哈密顿量的严格阳性。在证明如何与相应的障碍物配置协同之前，探索了这种常见方向性假设的基本后果，这会导致障碍物表面上的间隙不连续性并传播到自由空间中。最小的假设是对障碍物集的拓扑结构进行的。
We investigate the structure of discontinuities in clearance (or minimum time) functions for nonlinear control systems with general, closed obstacles (or targets). We establish general results regarding interactions between admissible trajectories and clearance discontinuities: e.g. instantaneous increases in clearance when passing through a discontinuity, and propagation of discontinuity along optimal trajectories. Then, investigating sufficient conditions for discontinuities, we explore a common directionality condition for velocities at a point, characterized by strict positivity of the minimal Hamiltonian. Elementary consequences of this common directionality assumption are explored before demonstrating how, in concert with corresponding obstacle configurations, it gives rise to clearance discontinuities both on the surface of the obstacle and propagating out into free space. Minimal assumptions are made on the topological structure of obstacle sets.
