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

TL;DR

Model Predictive Path Integral (MPPI) often yields jerky, high-variance controls unsuitable for agile fixed-wing aerial vehicles. pi-MPPI introduces a projection filter solved via a fast quadratic program (QP) to minimally adjust control samples, enforcing bounds on magnitude and derivatives, with a differentiable, ADMM-based solver and a self-supervised neural warm-start. A low-dimensional, polynomial control parametrization can further reduce projection size, enabling real-time operation. Empirical results on obstacle avoidance and terrain-following tasks show smoother trajectories, lower derivative constraint residuals, and improved robustness relative to baselines, with feasible computation times (~50 Hz) on standard hardware.

Abstract

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.

Figures (4)

• Figure 1: Our warm-start policy network. It consists of an MLP network and an unrolled chain of $L$ iterations of $\mathbf{f}_{FP}$. During training, the gradients flow through $\mathbf{f}_{FP}$, which ensures that the warm-start produced by MLP is aware of how it is going to be used by downstream $\mathbf{f}_{FP}$ ( steps \ref{['eqn:projection_cost']}-\ref{['eqn:projection_lambda']} )
• Figure 2: Benchmarks used to evaluate $\pi$-MPPI against baselines and comparison of computation-time. a) Obstacle avoidance scenario b) Terrain following scenario c) Computation time per MPC step. d) Computation time for solving \ref{['eqn:proj_nu_cost_qp']}-\ref{['slack']} with polynomial and way-point parametrization of $\overline{\boldsymbol{\nu}}^m$, for varying batch size and number of projection iterations.
• Figure 3: Plot of the optimal roll angle and its derivatives resulting from $\pi$-MPPI and baselines.
• Figure 4: Plot of the commanded roll angle across the first 50 MPC iteration for one of the experiments. It can be seen that our approach $\pi$-MPPI produces the smoothest profile that satisfies bounds on not only control values but also its first and second derivatives.

Theorems & Definitions (1)

• Remark 1