Safe Planning and Control Under Uncertainty: A Model-Free Design With One-Step Backward Data

Autonomous systems are desired to safely accomplish predetermined tasks with guaranteed performance despite uncertainties. This article proposes a safe planning and performance-guaranteed control (SP-PGC) scheme to accomplish safe execution of autonomous systems suffering from uncertainties and disturbances. This is realized by investigating mutual influences between planning and control levels, either explicitly considering control-level attainable performance bounds into safe planning algorithms, or directly relating planned safe boundaries to control-level performance bounds. In particular, we first utilize one-step backward data to construct incremental systems, which are equivalent representations of the investigated autonomous systems but without using explicit model information (kinematics and/or dynamics). The formulated incremental systems transform the influence of uncertainties and disturbances into the effect of provably bounded estimation errors, caused by the difference between current and one-step backward states. Then, we introduce the concept of input-to-state stable with provable safety barrier Lyapunov function (ISS-PS-BLF) to facilitate the performance-guaranteed tracking controller design based on the incremental systems, wherein the estimation errors are rigorously analyzed through an input-to-state stable approach. Finally, either the guaranteed tracking performance bound of the ISS-PS-BLF based controller is considered in the safe planning algorithm to guide the reference trajectory generation, or the safe planned boundary is used to determine the explicit value of the control-level performance bound for safe execution under uncertainty. The efficiency of our developed SP-PGC scheme is validated through both numerical and experimental validations.