$\pi$-MPPI: A Projection-Based Model Predictive Path Integral Scheme for Smooth Optimal Control of Fixed-Wing Aerial Vehicles

Model Predictive Path Integral (MPPI) is a popular sampling-based Model Predictive Control (MPC) algorithm for nonlinear systems. It optimizes trajectories by sampling control sequences and averaging them. However, a key issue with MPPI is the non-smoothness of the optimal control sequence, leading to oscillations in systems like fixed-wing aerial vehicles (FWVs). Existing solutions use post-hoc smoothing, which fails to bound control derivatives. This paper introduces a new approach: we add a projection filter π to minimally correct control samples, ensuring bounds on control magnitude and higher-order derivatives. The filtered samples are then averaged using MPPI, leading to our π-MPPI approach. We minimize computational overhead by using a neural accelerated custom optimizer for the projection filter. π-MPPI offers a simple way to achieve arbitrary smoothness in control sequences. While we focus on FWVs, this projection filter can be integrated into any MPPI pipeline. Applied to FWVs, π-MPPI is easier to tune than the baseline, resulting in smoother, more robust performance.