A Computationally Efficient Learning-Based Model Predictive Control for Multirotors under Aerodynamic Disturbances

TL;DR

This work tackles high-speed multirotor autonomy under unknown aerodynamic disturbances by marrying differential flatness with a learning-based MPC that uses Gaussian Processes to model drag as a function of the flat state. The disturbance GP is linearized around the predicted trajectory (LinGP) and probabilistic feasibility constraints are reformulated as second-order cone constraints, enabling a convex SOCP formulation solvable in real time. The approach jointly optimizes trajectory and control inputs, yielding dynamically feasible trajectories that account for drag, with simulation results showing substantial improvements in tracking accuracy (up to 55% error reduction) and robust feasibility across challenging drag conditions. Practically, this yields a computationally efficient, drag-aware planning/control framework suitable for real-time deployment on resource-constrained multirotors, with clear avenues for real-world validation and comparison to GP-MPC methods.

Abstract

Neglecting complex aerodynamic effects hinders high-speed yet high-precision multirotor autonomy. In this paper, we present a computationally efficient learning-based model predictive controller that simultaneously optimizes a trajectory that can be tracked within the physical limits (on thrust and orientation) of the multirotor system despite unknown aerodynamic forces and adapts the control input. To do this, we leverage the well-known differential flatness property of multirotors, which allows us to transform their nonlinear dynamics into a linear model. The main limitation of current flatness-based planning and control approaches is that they often neglect dynamic feasibility. This is because these constraints are nonlinear as a result of the mapping between the input, i.e., multirotor thrust, and the flat state. In our approach, we learn a novel representation of the drag forces by learning the mapping from the flat state to the multirotor thrust vector (in a world frame) as a Gaussian Process (GP). Our proposed approach leverages the properties of GPs to develop a convex optimal controller that can be iteratively solved as a second-order cone program (SOCP). In simulation experiments, our proposed approach outperforms related model predictive controllers that do not account for aerodynamic effects on trajectory feasibility, leading to a reduction of up to 55% in absolute tracking error.

Figures (6)

• Figure 1: Block diagram of our proposed learning-based MPC architecture. Our proposed approach: 1) learns the Force Disturbance Model$\mathbf{d}(\mathbf{z})$, as a Gaussian Process (GP), 2) linearizes the GP (LinGP) about the current predicted optimal trajectory $\mathbf{z}^{*}_{\text{traj}}$ and 3) develops a linear MPC that enables high performance while ensuring dynamic feasibility (probabilistically) which is efficiently solved as a second-order cone program (SOCP).
• Figure 2: Schematic of multirotor coordinate frames and the proposed constraints on thrust vector $\mathbf{T}$ (blue) in (\ref{['eq_ball']}) and (\ref{['eq_cone']}).
• Figure 3: Comparison of performance and input feasibility for multirotor subject to linear drag. We compare the (a) absolute path error and (b) thrust angle for increasingly aggressive sinusoidal trajectories using FMPC (red), SOCP No Learning (yellow) and our proposed SOCP Learning (blue). Our proposed approach outperforms similar methods that neglect the effects of drag on feasibility. The optimization for SOCP No Learning (yellow) goes infeasible for trajectories $\omega = 4.5$ and $\omega = 5.0$ (marked with a $\times$).
• Figure 4: Comparison of performance and input feasibility for multirotor subject to quadratic drag. We compare the (a) absolute path error and (b) thrust angle for increasingly aggressive sinusoidal trajectories using FMPC (red), SOCP No Learning (yellow) and our proposed SOCP Learning (blue). Our proposed approach outperforms similar methods that neglect the effects of drag on feasibility. The optimization for SOCP No Learning (yellow) goes infeasible for trajectories $\omega = 4.5$ and $\omega = 4.6$ (marked with a $\times$).
• Figure 5: Visualization of multirotor following sinusoidal trajectory with $\omega = 2$ rad/s subject to quadratic drag: (a) Comparison of path flown under SOCP No Learning (yellow) and our proposed SOCP Learning (blue); Thrust $\mathbf{T}$ and constraints for (b) SOCP No Learning and (c) SOCP Learning (proposed). We observe that our proposed approach sends larger feasible thrust commands to compensate for drag leading to reduced tracking errors.

Theorems & Definitions (1)

• Definition 1