  This paper presents a reactive navigation method that leverages a Model
Predictive Path Integral (MPPI) control enhanced with spline interpolation for
the control input sequence and Stein Variational Gradient Descent (SVGD). The
MPPI framework addresses a nonlinear optimization problem by determining an
optimal sequence of control inputs through a sampling-based approach. The
efficacy of MPPI is significantly influenced by the sampling noise. To rapidly
identify routes that circumvent large and/or newly detected obstacles, it is
essential to employ high levels of sampling noise. However, such high noise
levels result in jerky control input sequences, leading to non-smooth
trajectories. To mitigate this issue, we propose the integration of spline
interpolation within the MPPI process, enabling the generation of smooth
control input sequences despite the utilization of substantial sampling noises.
Nonetheless, the standard MPPI algorithm struggles in scenarios featuring
multiple optimal or near-optimal solutions, such as environments with several
viable obstacle avoidance paths, due to its assumption that the distribution
over an optimal control input sequence can be closely approximated by a
Gaussian distribution. To address this limitation, we extend our method by
incorporating SVGD into the MPPI framework with spline interpolation. SVGD,
rooted in the optimal transportation algorithm, possesses the unique ability to
cluster samples around an optimal solution. Consequently, our approach
facilitates robust reactive navigation by swiftly identifying obstacle
avoidance paths while maintaining the smoothness of the control input
sequences. The efficacy of our proposed method is validated on simulations with
a quadrotor, demonstrating superior performance over existing baseline
techniques.
