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Lipschitz Safe Bayesian Optimization for Automotive Control

Johanna Menn, Pietro Pelizzari, Michael Fleps-Dezasse, Sebastian Trimpe

TL;DR

The paper tackles safe controller tuning for automotive hardware under multiple safety constraints by proposing Multiple Constraints Lipschitz-only Safe BO (MCLoSBO). Building on Lipschitz-based safety, it replaces probabilistic RKHS-based guarantees with deterministic safety bounds using Lipschitz constants $L_i$ and bounded noise $E_i$, maintaining a safe set $S_n$ and expanding it via maximizers $M_n$ and expanders $G_n$ with a simple acquisition $\alpha(\boldsymbol{\theta},i)=u_{i,n}(\boldsymbol{\theta})-l_{i,n}(\boldsymbol{\theta})$. The approach supports asynchronous optimization and online hyperparameter tuning, and it extends SafeOpt-MC while ensuring safety for all iterations. Empirically, MCLoSBO matches or surpasses SafeOpt-MC in simulation and demonstrates safe, substantial performance gains when tuning a lateral trajectory-tracking controller on a real vehicle, validating both practical safety and effectiveness.

Abstract

Controller tuning is a labor-intensive process that requires human intervention and expert knowledge. Bayesian optimization has been applied successfully in different fields to automate this process. However, when tuning on hardware, such as in automotive applications, strict safety requirements often arise. To obtain safety guarantees, many existing safe Bayesian optimization methods rely on assumptions that are hard to verify in practice. This leads to the use of unjustified heuristics in many applications, which invalidates the theoretical safety guarantees. Furthermore, applications often require multiple safety constraints to be satisfied simultaneously. Building on recently proposed Lipschitz-only safe Bayesian optimization, we develop an algorithm that relies on readily interpretable assumptions and satisfies multiple safety constraints at the same time. We apply this algorithm to the problem of automatically tuning a trajectory-tracking controller of a self-driving car. Results both from simulations and an actual test vehicle underline the algorithm's ability to learn tracking controllers without leaving the track or violating any other safety constraints.

Lipschitz Safe Bayesian Optimization for Automotive Control

TL;DR

The paper tackles safe controller tuning for automotive hardware under multiple safety constraints by proposing Multiple Constraints Lipschitz-only Safe BO (MCLoSBO). Building on Lipschitz-based safety, it replaces probabilistic RKHS-based guarantees with deterministic safety bounds using Lipschitz constants and bounded noise , maintaining a safe set and expanding it via maximizers and expanders with a simple acquisition . The approach supports asynchronous optimization and online hyperparameter tuning, and it extends SafeOpt-MC while ensuring safety for all iterations. Empirically, MCLoSBO matches or surpasses SafeOpt-MC in simulation and demonstrates safe, substantial performance gains when tuning a lateral trajectory-tracking controller on a real vehicle, validating both practical safety and effectiveness.

Abstract

Controller tuning is a labor-intensive process that requires human intervention and expert knowledge. Bayesian optimization has been applied successfully in different fields to automate this process. However, when tuning on hardware, such as in automotive applications, strict safety requirements often arise. To obtain safety guarantees, many existing safe Bayesian optimization methods rely on assumptions that are hard to verify in practice. This leads to the use of unjustified heuristics in many applications, which invalidates the theoretical safety guarantees. Furthermore, applications often require multiple safety constraints to be satisfied simultaneously. Building on recently proposed Lipschitz-only safe Bayesian optimization, we develop an algorithm that relies on readily interpretable assumptions and satisfies multiple safety constraints at the same time. We apply this algorithm to the problem of automatically tuning a trajectory-tracking controller of a self-driving car. Results both from simulations and an actual test vehicle underline the algorithm's ability to learn tracking controllers without leaving the track or violating any other safety constraints.
Paper Structure (18 sections, 1 theorem, 13 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 18 sections, 1 theorem, 13 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related Work
  3. Preliminaries
  4. Gaussian processes
  5. Bayesian optimization
  6. Bayesian optimization with safety constraints
  7. Multiple constraint Lipschitz-only Safe BO
  8. Assumptions
  9. Algorithm
  10. Guarantees
  11. Practical adaptations
  12. Asynchronous optimization
  13. Hyperparameter optimization
  14. Application Study
  15. Experimental setup
  16. ...and 3 more sections

Key Result

Proposition 3

Given the Assumptions ass:lipschitz and ass:noise for any choice of $\beta \in \mathbb{R}^+$, the MCLoSBO algorithm yields a sequence of safe inputs, i.e., $g_i(\boldsymbol{\theta}_n) \geq 0$ for all $i=1, ..., q$ and $n \geq 1$.

Figures (5)

  • Figure 1: MCLoSBO is used to tune the parameters $\boldsymbol{\theta}$ of a lateral controller that is steering the vehicle (yellow arrow) to track the target trajectory (green) as closely as possible. The tracking performance is measured by $f(\boldsymbol{\theta})$. The optimization is sequential: MCLoSBO sets new safe parameters $\boldsymbol{\theta}_n$ that do not violate the safety constraints described by $g_i(\boldsymbol{\theta})$ (red). After one lap on the test track, the corresponding values of the performance function $f(\boldsymbol{\theta}_n)$ and safety functions $g_i(\boldsymbol{\theta}_n)$ are measured with noise.
  • Figure 2: Illustration of MCLoSBO. The true performance function $f(\boldsymbol{\theta})$ (gray) and the true safety function $g_1(\boldsymbol{\theta})$ (gray) are queried in each iteration (blue dots). Based on the measurements, the safe set is determined following \ref{['safesetMCLoSBO']} (orange). The functions are modeled by GPs (blue). The next query is chosen by evaluating the acquisition function in the maximizer set (violet) and expander sets (green).
  • Figure 3: LEFT: Test track with the speed profile of the experiment (color bar) in $km/h$. The simulation is started at the position $T_0$, and the disturbance is injected at $T_1=100$. The simulation ends at $T_2=120$ at the same position as $T_0$. This time scale corresponds to the time axis of the right plot. RIGHT: Plot of the cross-track error over time of an optimization with one parameter. The optimized controller is blue, the initial controller is green, and the intermediate optimization steps are grey. The red line represents parameters not queried in the optimization that violate $g_2$.
  • Figure 4: Simulation results for optimizing parameter sets of one (a), two (b), and three (c) parameters. In (a), the green and the blue line are overlapping.
  • Figure 5: Results of the first vehicle experiment. No safety violations occur. The initial safe parameter is $\theta_0 = 0.3$. The red point is the last point of the optimization. These plots are generated in real time during the test and can be inspected by the test copilot. The gray points experiments represent the falsely measured points corrected based on the logging data.

Theorems & Definitions (2)

  • Proposition 3
  • proof