Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic\n Autonomous Systems

摘要

In this paper, we address the problem of uncertainty propagation through\nnonlinear stochastic dynamical systems. More precisely, given a discrete-time\ncontinuous-state probabilistic nonlinear dynamical system, we aim at finding\nthe sequence of the moments of the probability distributions of the system\nstates up to any desired order over the given planning horizon. Moments of\nuncertain states can be used in estimation, planning, control, and safety\nanalysis of stochastic dynamical systems. Existing approaches to address moment\npropagation problems provide approximate descriptions of the moments and are\nmainly limited to particular set of uncertainties, e.g., Gaussian disturbances.\nIn this paper, to describe the moments of uncertain states, we introduce\ntrigonometric and also mixed-trigonometric-polynomial moments. Such moments\nallow us to obtain closed deterministic dynamical systems that describe the\nexact time evolution of the moments of uncertain states of an important class\nof autonomous and robotic systems including underwater, ground, and aerial\nvehicles, robotic arms and walking robots. Such obtained deterministic\ndynamical systems can be used, in a receding horizon fashion, to propagate the\nuncertainties over the planning horizon in real-time. To illustrate the\nperformance of the proposed method, we benchmark our method against existing\napproaches including linear, unscented transformation, and sampling based\nuncertainty propagation methods that are widely used in estimation, prediction,\nplanning, and control problems.\n