Hongyu Nie

Qi Wei, Jianfeng Tao, Hongyu Nie et al.

Parallel simulation and control of large-scale robotic systems often rely on partitioned time stepping, yet finite-iteration coupling can inject spurious energy by violating power consistency--even when each subsystem is passive. This letter proposes a novel energy-safe, early-terminable iterative coupling for port-Hamiltonian subsystems by embedding a Douglas--Rachford (DR) splitting scheme in scattering (wave) coordinates. The lossless interconnection is enforced as an orthogonal constraint in the wave domain, while each subsystem contributes a discrete-time scattering port map induced by its one-step integrator. Under a discrete passivity condition on the subsystem time steps and a mild impedance-tuning condition, we prove an augmented-storage inequality certifying discrete passivity of the coupled macro-step for any finite inner-iteration budget, with the remaining mismatch captured by an explicit residual. As the inner budget increases, the partitioned update converges to the monolithic discrete-time update induced by the same integrators, yielding a principled, adaptive accuracy--compute trade-off, supporting energy-consistent real-time parallel simulation under varying computational budgets. Experiments on a coupled-oscillator benchmark validate the passivity certificates at numerical roundoff (on the order of 10e-14 in double precision) and show that the reported RMS state error decays monotonically with increasing inner-iteration budgets, consistent with the hard-coupling limit.

Qi Wei, Jianfeng Tao, Haoyang Tan et al.

Numerical optimal control is commonly divided between globally structured but dimensionally intractable Hamilton-Jacobi-Bellman (HJB) methods and scalable but local trajectory optimization. We introduce the Featurized Occupation Measure (FOM), a finite-dimensional primal-dual interface for the occupation-measure formulation that unifies trajectory search and global HJB-type certification. FOM is broad yet numerically tractable, covering both explicit weak-form schemes and implicit simulator- or rollout-based sampling methods. Within this framework, approximate HJB subsolutions serve as intrinsic numerical certificates to directly evaluate and guide the primal search. We prove asymptotic consistency with the exact infinite-dimensional occupation-measure problem, and show that for block-organized feasible certificates, finite-dimensional approximation preserves certified lower bounds with blockwise error and complexity control. We also establish persistence of these lower bounds under time shifts and bounded model perturbations. Consequently, these structural properties render global certificates into flexible, reusable computational objects, establishing a systematic basis for certificate-guided optimization in nonlinear control.

Hongyu Nie, Xu Liu, Zhaotong Tan et al.

Autonomous navigation in mobile robots, reliant on perception and planning, faces major hurdles in large-scale, complex environments. These include heavy computational burdens for mapping, sensor occlusion failures for UAVs, and traversal challenges on irregular terrain for UGVs, all compounded by a lack of perception-aware strategies. To address these challenges, we introduce Random Mapping and Random Projection (RMRP). This method constructs a lightweight linear parametric map by first mapping data to a high-dimensional space, followed by a sparse random projection for dimensionality reduction. Our novel Residual Energy Preservation Theorem provides theoretical guarantees for this process, ensuring critical geometric properties are preserved. Based on this map, we propose the RPATR (Robust Perception-Aware Trajectory Planner) framework. For UAVs, our method unifies grid and Euclidean Signed Distance Field (ESDF) maps. The front-end uses an analytical occupancy gradient to refine initial paths for safety and smoothness, while the back-end uses a closed-form ESDF for trajectory optimization. Leveraging the trained RMRP model's generalization, the planner predicts unobserved areas for proactive navigation. For UGVs, the model characterizes terrain and provides closed-form gradients, enabling online planning to circumvent large holes. Validated in diverse scenarios, our framework demonstrates superior mapping performance in time, memory, and accuracy, and enables computationally efficient, safe navigation for high-speed UAVs and UGVs. The code will be released to foster community collaboration.