Scalability and robustness of abstraction-based control for bipedal robots

Details

Supervisors

Jungers, Raphaël M.

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil électromécanicien, à finalité spécialisée: mécatronique

Abstract

enAbstraction-based control has emerged as a promising framework for the synthesis of correct-by-design controllers for nonlinear and hybrid systems. However, applying such methods to bipedal robots remains challenging due to the high dimensionality and complexity of their dynamics. This thesis investigates the scalability and robustness of abstraction-based control for a planar five-link biped robot using the Dionysos.jl framework. Since the computational cost of abstraction generation grows exponentially with the dimension of the state space, several strategies are explored to mitigate the curse of dimensionality. These include distributed transition computation through job arrays, exploitation of left–right symmetry, pruning techniques, and adaptive refinement strategies based on local sensitivity and Lipschitz estimates. The robustness of the generated abstractions is analysed through discretization error propagation and local Lipschitz bounds, with the objective of improving the reliability and precision of the synthesized controllers while limiting computational complexity. Different abstraction resolutions and model simplifications are evaluated in simulation to analyse the trade-offs between robustness, scalability, and control performance. The results highlight both the potential and the limitations of abstraction-based control for bipedal locomotion, and provide insights into practical strategies for improving the scalability of symbolic control methods applied to high-dimensional robotic systems.