An Approximate LQR Law With Range Feedback for State and Control Constrained Problems

ABSTRACT An optimal control problem with state and control constraints is addressed using a barrier function approach adapted from an interior‐point method. A closed‐form approximate Linear Quadratic Regulator (LQR) control law has been derived to achieve stabilizing behavior in a state and control constrained environment. The closed‐form control law provides automatic controller caution and safe steering . The controller caution is achieved by auto‐tuning and to adjust the system's transient response, and the safe steering is achieved by an automatic shift in the target point to avoid converging on an infeasible state. This work demonstrates the results on linear and non‐linear systems in comparison with the widely used Artificial Potential Field (APF) Method and the state‐of‐the‐art Control Barrier Function (CBF) method, both paired with the stabilizing LQR law. The proposed law also attains the guidance attribute in the proposed law by integrating range sensors for state constraint feedback. This is supported by the ROS‐Gazebo simulation results on a linear omnidirectional autonomous mobile robot with range sensor feedback for navigation in a structured environment.