Gaussian control barrier functions : A Gaussian process based approach to safety for robots
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In recent years, the need for safety of autonomous and intelligent robots has increased. Today, as robots are being increasingly deployed in closer proximity to humans, there is an exigency for safety since human lives may be at risk, e.g., self-driving vehicles or surgical robots. The objective of this thesis is to present a safety framework for dynamical systems that leverages tools from control theory and machine learning. More formally, the thesis presents a data-driven framework for designing safety function candidates which ensure properties of forward invariance. The potential benefits of the results presented in this thesis are expected to help applications such as safe exploration, collision avoidance problems, manipulation tasks, and planning, to name some. We utilize Gaussian processes (GP) to place a prior on the desired safety function candidate, which is to be utilized as a control barrier function (CBF). The resultant formulation is called Gaussian CBFs and they reside in a reproducing kernel Hilbert space. A key concept behind Gaussian CBFs is the incorporation of both safety belief as well as safety uncertainty, which former barrier function formulations did not consider. This is achieved by using robust posterior estimates from a GP where the posterior mean and variance serve as surrogates for the safety belief and uncertainty respectively. We synthesize safe controllers by framing a convex optimization problem where the kernel-based representation of GPs allows computing the derivatives in closed-form analytically. Finally, in addition to the theoretical and algorithmic frameworks in this thesis, we rigorously test our methods in hardware on a quadrotor platform. The platform used is a Crazyflie 2.1 which is a versatile palm-sized quadrotor. We provide our insights and detailed discussions on the hardware implementations which will be useful for large-scale deployment of the techniques presented in this dissertation.