Differentiable LQR as a Structured Policy Output Layer for Mapless Goal-Reaching Navigation of a Mobile Robot

Abstract

This paper addresses the problem of moving a mobile robot to a given goal in an unknown environment using local sensory data. A standard MLP policy trained with the PPO algorithm and directly generating linear and angular velocity commands is considered as the baseline approach. The proposed method is a policy architecture whose actor output is augmented with a differentiable linear–quadratic regulator layer. This architecture implements a two-level control generation scheme: the neural component of the policy produces a local control intention, while the embedded LQR layer transforms it into the final control action. The paper describes how this layer can be integrated into a continuous actor–critic policy without changing the environment action space and without moving the regulator outside the policy itself. Experimental evaluation is performed in ROS2/Gazebo using a TurtleBot3 robot in goal-reaching tasks in a free environment and in an environment with static obstacles. The comparison is conducted under a unified setup with identical observations, reward function, training and evaluation protocol, and metrics. The obtained results show that the proposed architecture does not degrade the robot’s basic ability to reach the goal and, in a more complex environment, produces a meaningful difference in behavior and trajectory quality compared with a standard MLP policy, which makes the embedded differentiable LQR layer a promising direction for further research.