High-Performance Model Predictive Control for Quadcopters with Formal Stability Guarantees

TL;DR

This work tackles fast, constrained quadcopter trajectory tracking by cascading a discrete-time, time-varying constraint-aware MPC for the outer translational dynamics with an inside nonlinear attitude controller that is uniformly locally exponentially stable and uniformly globally asymptotically stable. The outer loop explicitly accounts for total thrust limits and inter-sample behavior, using a 12th-order translational model decomposed into three 4th-order channels, and employs a non-quadratic terminal cost to guarantee UGAS without excessive conservatism. Formal stability is established for the full cascade, combining UGAS of the outer loop with UaGAS of the inner loop, and is corroborated by numerical and high-fidelity Avular simulations showing improved tracking accuracy and robustness over baselines and PID cascades. The approach reduces conservatism relative to prior MPC schemes with stability guarantees while delivering practical performance gains suitable for real-time onboard implementation.

Abstract

In this paper, we present a novel cascade control structure with formal guarantees of uniform almost global asymptotic stability for the state tracking error dynamics of a quadcopter. The proposed approach features a model predictive control strategy for the outer loop, explicitly accounting for the non-zero total thrust constraint. The outer-loop controller generates an acceleration reference, which is then converted into attitude, angular velocity and acceleration references, subsequently tracked by a nonlinear inner-loop controller. The proposed cascade control strategy is validated through numerical case studies, underlying high-fidelity models, demonstrating its ability to track fast trajectories with small error.

Figures (6)

• Figure 2: Schematic of TV constraints on $a_d$ in 3D. The radius of each sphere varies with the reference thrust $\bar{T}$, so the sphere with radius $\bar{T}(t)-\delta$ is not always the smaller one. The cube illustrates the decoupled constraint, limiting each of the components of $a_d$ to be within $\pm \Delta(t)$.
• Figure 3: Position errors $\Tilde{p}=[\Tilde{p}_x, \Tilde{p}_y, \Tilde{p}_z]$ for each axes.
• Figure 4: Desired accelerations in $x$, $y$, and $z$ during the first 10 seconds of the simulations. (a) shows that the Proposed MPC keeps $a_{d,i}$ within $- \Delta(t)$ to $\Delta(t)$, satisfying constraint (\ref{['TV cons decoupled']}). (b) shows the Baseline MPC, where $a_{d,i}$ are constrained within $- \Delta$ to $\Delta$, reflecting its conservative nature.
• Figure 5: 3D plot of the reference and actual trajectories, using the Avular high-fedility simulation environment. The reference trajectory is indicated in red across both cases.
• Figure 6: Position errors $\Tilde{p}=[\Tilde{p}_x, \Tilde{p}_y, \Tilde{p}_z]$ for each axes, using the Avular high-fedility simulation environment.

Theorems & Definitions (8)

• Lemma 2
• Lemma 3
• Lemma 4
• Theorem 3
• Lemma 5
• Theorem 4
• Theorem 5
• Corollary 1