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This tutorial paper presents recent work of the authors that extends thetheory of Control Barrier Functions (CBFs) to address practical challenges inthe synthesis of safe controllers for autonomous systems and robots. We presentnovel CBFs and methods that handle safety constraints (i) with time and inputconstraints under disturbances, (ii) with high-relative degree underdisturbances and input constraints, and (iii) that are affected by adversarialinputs and sampled-data effects. We then present novel CBFs and adaptationmethods that prevent loss of validity of the CBF, as well as methods to tunethe parameters of the CBF online to reduce conservatism in the system response.We also address the pointwise-only optimal character of CBF-induced controlinputs by introducing a CBF formulation that accounts for future trajectories,as well as implementation challenges such as how to preserve safety when usingoutput feedback control and zero-order-hold control. Finally we consider how tosynthesize non-smooth CBFs when discontinuous inputs and multiple constraintsare present.

Advances in the Theory of Control Barrier Functions: Addressing Practical Challenges in Safe Control Synthesis for Autonomous and Robotic Systems