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Inherently robust suboptimal MPC for autonomous racing with anytime feasible SQP

Logan Numerow, Andrea Zanelli, Andrea Carron, Melanie N. Zeilinger

TL;DR

This paper relies on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility.

Abstract

In recent years, the increasing need for high-performance controllers in applications like autonomous driving has motivated the development of optimization routines tailored to specific control problems. In this paper, we propose an efficient inexact model predictive control (MPC) strategy for autonomous miniature racing with inherent robustness properties. We rely on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility. In this way, we provide a strategy that computes suboptimal and yet feasible solutions with a computational footprint that is much lower than state-of-the-art methods based on the computation of locally optimal solutions. Under suitable assumptions on the terminal set and on the controllability properties of the system, we can state that, for any sufficiently small disturbance affecting the system's dynamics, recursive feasibility can be guaranteed. We validate the effectiveness of the proposed strategy in simulation and by deploying it onto a physical experiment with autonomous miniature race cars. Both the simulation and experimental results demonstrate that, using the feasible SQP method, a feasible solution can be obtained with moderate additional computational effort compared to strategies that resort to early termination without providing a feasible solution. At the same time, the proposed method is significantly faster than the state-of-the-art solver Ipopt.

Inherently robust suboptimal MPC for autonomous racing with anytime feasible SQP

TL;DR

This paper relies on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility.

Abstract

In recent years, the increasing need for high-performance controllers in applications like autonomous driving has motivated the development of optimization routines tailored to specific control problems. In this paper, we propose an efficient inexact model predictive control (MPC) strategy for autonomous miniature racing with inherent robustness properties. We rely on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility. In this way, we provide a strategy that computes suboptimal and yet feasible solutions with a computational footprint that is much lower than state-of-the-art methods based on the computation of locally optimal solutions. Under suitable assumptions on the terminal set and on the controllability properties of the system, we can state that, for any sufficiently small disturbance affecting the system's dynamics, recursive feasibility can be guaranteed. We validate the effectiveness of the proposed strategy in simulation and by deploying it onto a physical experiment with autonomous miniature race cars. Both the simulation and experimental results demonstrate that, using the feasible SQP method, a feasible solution can be obtained with moderate additional computational effort compared to strategies that resort to early termination without providing a feasible solution. At the same time, the proposed method is significantly faster than the state-of-the-art solver Ipopt.
Paper Structure (14 sections, 1 theorem, 31 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 14 sections, 1 theorem, 31 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contribution
  3. Notation
  4. System Model
  5. Optimal control problem formulation
  6. Feasible sequential quadratic programming
  7. Inherently robust anytime MPC
  8. Terminal Set Computation
  9. Inherently robust recursive feasibility
  10. Experiments
  11. Simulation Setup
  12. Hardware Setup
  13. Results
  14. Conclusions

Key Result

Proposition V.6

Let Assumptions assum:lip_dyn-assum:sigma hold. Moreover, let $x$ be such that $\mathcal{P}(x, t)$ is feasible and let $\tilde{u}_{x}$ be a feasible solution to $\mathcal{P}(x,t)$. For any positive integer $M \geq 0$, there exists a positive constant $\delta$, such that if $w = \{w_0, w_1, \cdots\}$

Figures (7)

  • Figure 1: Kyosho Mini-Z 1:28 scale miniature race car.
  • Figure 2: Terminal manifold (blue) based on a discrete feasible periodic trajectory, with example trajectories (green) satisfying the terminal constraint.
  • Figure 3: Illustration of time-varying terminal set and deadbeat controller.
  • Figure 4: Illustration of the construction of the feasible candidate in the proof of Proposition \ref{['prop:main_prop']}. Choosing $\tilde{\sigma} \cdot \delta + \sigma \leq \rho$ we can apply the deadbeat controller from Assumption \ref{['assum:deadbeat']} in order to construct a feasible candidate and guarantee recursive feasibility.
  • Figure 5: Race track used in simulation and hardware experiments, with closed-loop trajectories from hardware experiment HW1 colored according to forward velocity $v_f$.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Remark V.3
  • Remark V.5
  • Proposition V.6: $M$-step open-loop recursive feasibility
  • proof