MechE PhD Prospectus Defense | Shuo Liu

TITLE: SAFETY-CRITICAL OPTIMAL CONTROL USING CONTROL BARRIER FUNCTIONS

ABSTRACT: Control Barrier Functions (CBFs) are widely used to ensure safety in robots or autonomous systems. By defining safe sets in the system’s state space, CBFs ensure that the system remains within these sets during operation, preventing unsafe behaviors like collisions. CBFs work by modifying control inputs to enforce safety constraints in real-time, often through optimization techniques. This proposal addresses several key challenges associated with CBFs across various areas, including optimization, control, plan-ning, and navigation. This proposal consists of three parts. In Part I, we identify the optimization infeasibility between Con-trol Barrier Function (CBF) constraints and input constraints, and introduce an Auxiliary-Variable Based Control Barrier Function (AVCBF) to address feasibility issues in optimal control within a Quadratic Pro-gramming (QP) framework. Specifically, we introduce an auxiliary variable that multiplies each CBF itself, and define dynamics for the auxiliary variable to adapt it in constructing the corresponding CBF constraint. In this way, we can improve the feasibility of the CBF-based QP while avoiding extensive parameter tuning. Additionally, the auxiliary variable enables the definition of a feasibility constraint, en-forced through a CBF-based equation applicable to general affine control systems, thereby ensuring both feasibility and safety under tight control constraints. We observe that incorporating discrete-time CBFs (DCBFs) within a nonlinear Model Predictive Con-trol (NMPC) framework can enhance both safety and feasibility [1], as it leverages future state information along a receding horizon to improve current control decisions. However, this approach results in heavy computation due to the nonconvex nature of the NMPC-DCBF optimization problem. In Part II, we address this by developing an iterative MPC (iMPC) with discrete-time high-order CBFs (DHOCBFs), which improves computational efficiency while maintaining strong safety and feasibility. Additionally, we extend this method using machine learning to handle complex-shaped obstacle avoidance in confined environments. In Part III, We discuss future work focused on applying our proposed methods to motion planning and navigation applications. One challenging scenario is enabling the end effector of a robotic manipulator to reach a target position without colliding with obstacles. This problem is difficult due to factors such as high dimensionality and complex dynamics, joint limits and physical constraints, and the interdependence of variables. These complexities make it challenging to design effective control strategies that ensure safe, precise movement while avoiding obstacles. We are also interested in applying the proposed algorithms to other scenarios, such as autonomous racing and traffic merging.

COMMITTEE: ADVISOR/CHAIR Professor Calin Belta, ME/SE/ECE; Professor Roberto Tron, ME/SE; Professor Christos Cassandras, SE/ECE; Professor Sean Andersson, ME/SE