Existing trajectory planning methods often face challenges in ensuring stable robot motion control, leading to significant positional errors during navigation. This study proposes Timed-Elastic-Band-Based Variable Splitting (TEB-VS), a novel framework that integrates variable splitting (VS)—a constrained optimization technique—with the classical Timed-Elastic-Band (TEB) algorithm. Unlike incremental modifications to TEB, TEB-VS introduces a systematic combination of VS and TEB to decompose non-convex global constraints into tractable subproblems while leveraging symmetry principles for balanced multi-objective control (e.g., velocity, acceleration, and obstacle avoidance). Experimental results demonstrate that TEB-VS achieves a $46.5\%$ improvement in motion stability over traditional TEB in obstacle-free simulations and a $37\%$ enhancement in dynamic obstacle scenarios. Real-world tests show a $26.7\%$ reduction in angular velocity oscillations, with computational efficiency comparable to TEB. The framework’s effectiveness in harmonizing trajectory smoothness and dynamic adaptability is validated through extensive simulations and TurtleBot2 experiments.

Recent advancements in lightweight electroencephalogram(EEG) signal classification have enabled real-time human–robot interaction, yet challenges persist in balancing computational efficiency and safety in dynamic path planning. This study proposes an EEG-based inverse reinforcement learning (EIRL) framework to simulate human navigation strategies by decoding neural decision preferences. The method integrates a pruned WNFG-SSCCNet-ADMM classifier for EEG signal mapping, apprenticeship learning for reward function extraction, and Q-learning for policy optimization. Experimental validation in an 8 × 8 FrozenLake-v1 environment demonstrates that EIRL reduces average path risk values by 50% compared with traditional reinforcement learning, achieving expert-level safety ($\Delta$ = 4) while maintaining optimal path lengths. The framework enhances adaptability in unknown environments by embedding human-like risk aversion into robotic planning, offering a robust solution for applications requiring minimal prior environmental knowledge. Results highlight the synergy between neural feedback and computational models, advancing inclusive human–robot collaboration in safety-critical scenarios.

Existing trajectory planning methods are struggling to handle the issue of autonomous track swinging during navigation, resulting in significant errors when reaching the destination. In this article, we address autonomous trajectory planning problems, which aims at developing innovative solutions to enhance the adaptability and robustness of unmanned systems in navigating complex and dynamic environments. We first introduce the variable splitting (VS) method as a constrained optimization method to reimagine the renowned Timed-Elastic-Band (TEB) algorithm, resulting in a novel collision avoidance approach named Timed-Elastic-Band based variable splitting (TEB-VS). The proposed TEB-VS demonstrates superior navigation stability, while maintaining nearly identical resource consumption to TEB. We then analyze the convergence of the proposed TEB-VS method. To evaluate the effectiveness and efficiency of TEB-VS, extensive experiments have been conducted using TurtleBot2 in both simulated environments and real-world datasets.