Bayesian Optimization with Temporal Logic Constraints for Automated GNC Tuning
Creators: name:  R. POLONIO 
name:   C. ARDURA 
name:   L. HEWING 
name:   V. PREDA 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT DYNAMICS
GNC
AVIONICS
OPTIMIZATION

description: Automated tuning the control of dynamic systems has been a long-standing challenge and continues to be an active research field. Classical auto-tuning methods for control typically target simple SISO structures such as PID control [1]. For complex dynamical systems, such as in guidance navigation and control, on the other hand, the relationship between parameterization and achieved performance often becomes prohibitively hard to express concisely, and the traditional approaches are not applicable. In these settings, tuning is typically carried out using Monte Carlo type (simulation) experiments, which can be computationally expensive and subject to considerable noise, hindering a straightforward judgement on the performance and robustness of a given system parameterization. These issues make data efficiency, as well as the effects of noise and uncertainty dominating issues for a successful automated tuning, motivating the use of data-efficient stochastic black-box optimization strategies such as Bayesian optimization (BO). BO aims to reduce the number of (simulation) experiments and inherently takes noisy function evaluations into account [2], by relying on stochastic surrogate function models in the form of GP regression [3]. In the context of controller learning, BO can be understood as aiming at optimizing a closed-loop performance metric cost J(x) as a mapping of the controller parameters x, which is evaluated over a sequence of finite-time experiments and has gathered significant attention in recent years [4]. Given the flexibility of this framework, it is then attractive to use the approach to tune with respect to high-level requirements, which we express via temporal logic expressions. Temporal logic provides a framework combining familiar (Boolean) logical operations with temporal modalities to describe a rich set of specifications, based e.g. on the output signals of a system evolving over time. This allows for the precise expressions of requirements and subsequent formal manipulation, enabling the development of automated and systematic design and verification methods. We employ quantitative semantics of such expression to formulate the requirements as constraints in our black-box optimization [5], arriving at an algorithm that efficiently explores the parameter regions to maximize the performance while satisfying temporal logic requirements in the form of constraints. We illustrate the effectiveness of the developed algorithms on a sophisticated GNC functional engineering simulator environment of a parafoil system during landing. This benchmark is based on the Space Rider descend and landing phase, the GNC software of which is being developed in-house at SENER Aeroespacial. We demonstrate and analyse how different major sources of disturbances and uncertainty, such as wind conditions that are only partially known, affect the GNC performance and how the developed tool can be used to arrive at a robust parameterization. Our results, finally, show how temporal logic constrained BO can be efficiently used to improve system performance, explore parameter interdependencies and provide valuable insights to support the tuning of GNC systems to fulfil complex requirements. References [1] K. J. Astrom, T. Hagglund, C. C. Hang and W. K. Ho, Automatic tuning and adaptation for PID controllers - a survey, Control Engineering Practice 1, 699-714 (1993) [2] B. Shahriari, K. Swersky, Z. Wang, R. P. Adams and N. de Freitas, Taking the Human Out of the Loop: A Review of Bayesian Optimization, Proc. IEEE 104, 148-175 (2016) [3] C. E. Rasmussen and C. K. I. Williams, Gaussian processes for machine learning, MIT Press (2006) [4] M. Neumann-Brosig, A. Marco, D. Schwarzmann, S. Trimpe, Data-Efficient Autotuning With Bayesian Optimization: An Industrial Control Study, IEEE Trans. Control Systems Technology 28, 730-740 (2020) [5] J. R. Gardner, M. J. Matt, Z. E. Xu, K. Q. Weinberger, and J. P. Cunningham. \"Bayesian Optimization with Inequality Constraints,\" ICML 32, 937-945 (2014)