Bingxian Wu

Yicheng Lin, Bingxian Wu, Nan Bai et al.

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics through a lifted state space, the presence of approximation error inevitably leads to deviations in the computed optimal controller and the resulting value function. We derive explicit upper bounds for these optimality deviations, which characterize the worst-case effect of approximation error. Supported by numerical examples, these theoretical findings provide a quantitative foundation for improving the robustness of data-driven optimal controller design.

Yicheng Lin, Bingxian Wu, Nan Bai et al.

The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This raises a distinct and fundamental question on optimality robustness, specifically, how uncertainties affect the optimal solution itself. To address this problem, we adopt a unified analysis-to-design perspective for systematically quantifying and improving optimality robustness. At the analysis level, we derive explicit upper bounds on the deviations of both the value function and the optimal controller, where uncertainties from multiple sources are systematically integrated into a unified norm-bounded representation. At the design level, we develop a robustness-aware optimal control methodology that provably reduces such optimality deviations, thereby enhancing robustness while explicitly revealing a quantitative trade-off between nominal optimality and robustness. As for practical implementation aspect, we further propose a tractable policy iteration algorithm, whose well-posedness and convergence are established via vanishing viscosity regularization and elliptic partial differential equation (PDE) techniques. Numerical examples validate the theoretical findings and demonstrate the effectiveness of proposed methodology.

Pengying Wu, Yao Mu, Bingxian Wu et al.

In the realm of household robotics, the Zero-Shot Object Navigation (ZSON) task empowers agents to adeptly traverse unfamiliar environments and locate objects from novel categories without prior explicit training. This paper introduces VoroNav, a novel semantic exploration framework that proposes the Reduced Voronoi Graph to extract exploratory paths and planning nodes from a semantic map constructed in real time. By harnessing topological and semantic information, VoroNav designs text-based descriptions of paths and images that are readily interpretable by a large language model (LLM). In particular, our approach presents a synergy of path and farsight descriptions to represent the environmental context, enabling LLM to apply commonsense reasoning to ascertain waypoints for navigation. Extensive evaluation on HM3D and HSSD validates VoroNav surpasses existing benchmarks in both success rate and exploration efficiency (absolute improvement: +2.8% Success and +3.7% SPL on HM3D, +2.6% Success and +3.8% SPL on HSSD). Additionally introduced metrics that evaluate obstacle avoidance proficiency and perceptual efficiency further corroborate the enhancements achieved by our method in ZSON planning. Project page: https://voro-nav.github.io