Predictive Control Barrier Functions for Online Safety Critical Control

Abstract

This paper presents a methodology for constructing Control Barrier Functions (CBFs) that proactively consider the future safety of a system along a nominal trajectory, and effect corrective action before the trajectory leaves a designated safe set. Specifically, this paper presents a systematic approach for propagating a nominal trajectory on a receding horizon, and then encoding the future safety of this trajectory into a CBF. If the trajectory is unsafe, then a controller satisfying the CBF condition will modify the nominal trajectory before the trajectory becomes unsafe. Compared to existing CBF techniques, this strategy is proactive rather than reactive and thus potentially results in smaller modifications to the nominal trajectory. The proposed strategy is shown to be provably safe, and then is demonstrated in simulated scenarios where it would otherwise be difficult to construct a traditional CBF. In simulation, the predictive CBF results in less modification to the nominal trajectory and smaller control inputs than a traditional CBF, and faster computations than a nonlinear model predictive control approach.

Rate-Tunable Control Barrier Functions: Methods and Algorithms for Online Adaptation

“…[35] propose a future-focused CBF, wherein they construct a CBF based on the minimum distance to the boundary of unsafe set in the future predicted based on zero acceleration policy. [36] also proposes a predictive control barrier function (PCBF) that, given a nominal trajectory in terms of sequence of control inputs, predicts the future and upon encountering a safety violation, uses the sensitivity of state at the future instant of safety violation w.r.t the first input in the sequence to reduce the violation.…”

“…All of the aforementioned works except for [35] and [36] perform offline analysis (training or verification) to find a control barrier function. Since it is computationally infeasible to simulate all possible scenarios offline that the robotic agent may be subjected while operating in real-world, there is a need for online learning and adaptation in face of unforeseen environments.…”

“…the parameters which can be obtained by performing sensitivity analysis of QPs which is readily implemented in libraries such as cvxpy [50]. The chain-rule based recursive analysis that we employ in ( 34)- (36) to compute gradients of stage-wise reward w.r.t the parameter θ is amenable to backpropagation-based derivative computation and is also readily implementable in libraries like pytorch and tensorflow, that are capable of constructing computational graphs. The gradient of other quantities of interest, such as barrier function, can be obtained similarly.…”