  Robotic navigation in unknown, cluttered environments with limited sensing
capabilities poses significant challenges in robotics. Local trajectory
optimization methods, such as Model Predictive Path Intergal (MPPI), are a
promising solution to this challenge. However, global guidance is required to
ensure effective navigation, especially when encountering challenging
environmental conditions or navigating beyond the planning horizon. This study
presents the GP-MPPI, an online learning-based control strategy that integrates
MPPI with a local perception model based on Sparse Gaussian Process (SGP). The
key idea is to leverage the learning capability of SGP to construct a variance
(uncertainty) surface, which enables the robot to learn about the navigable
space surrounding it, identify a set of suggested subgoals, and ultimately
recommend the optimal subgoal that minimizes a predefined cost function to the
local MPPI planner. Afterward, MPPI computes the optimal control sequence that
satisfies the robot and collision avoidance constraints. Such an approach
eliminates the necessity of a global map of the environment or an offline
training process. We validate the efficiency and robustness of our proposed
control strategy through both simulated and real-world experiments of 2D
autonomous navigation tasks in complex unknown environments, demonstrating its
superiority in guiding the robot safely towards its desired goal while avoiding
obstacles and escaping entrapment in local minima. The GPU implementation of
GP-MPPI, including the supplementary video, is available at
https://github.com/IhabMohamed/GP-MPPI.
