  This paper presents an off-policy Gaussian Predictive Control (GPC) framework
aimed at solving optimal control problems with a smaller computational
footprint, thereby facilitating real-time applicability while ensuring critical
safety considerations. The proposed controller imitates classical control
methodologies by modeling the optimization process through a Gaussian process
and employs Gaussian Process Regression to learn from the Model Predictive
Control (MPC) algorithm. Notably, the Gaussian Process setup does not
incorporate a built-in model, enhancing its applicability to a broad range of
control problems. We applied this framework experimentally to a differential
drive mobile robot, tasking it with trajectory tracking and obstacle avoidance.
Leveraging the off-policy aspect, the controller demonstrated adaptability to
diverse trajectories and obstacle behaviors. Simulation experiments confirmed
the effectiveness of the proposed GPC method, emphasizing its ability to learn
the dynamics of optimal control strategies. Consequently, our findings
highlight the significant potential of off-policy Gaussian Predictive Control
in achieving real-time optimal control for handling of robotic systems in
safety-critical scenarios.
