motion planning

This work proposes an online trajectory generation method based on piecewise quintic/quartic splines to address the challenge of converting arbitrary geometric paths into kinematically feasible and collision-free trajectories in dynamic environments. The approach explicitly enforces jerk constraints and supports real-time replanning under high-frequency goal updates. By integrating dynamic environment perception and a responsive adaptation mechanism, it guarantees collision avoidance within finite time while permitting bounded deviations from the original path. Both simulation and real-world experiments demonstrate that the method outperforms existing approaches in trajectory smoothness, computational efficiency, and real-time performance, achieving stable operation in human-in-the-loop dynamic scenarios with target update rates up to 1 kHz.

Efficient and smooth collision-free trajectory planning in complex environments remains a fundamental challenge in robotics. Existing corridor-based approaches are constrained by the quality of free-space decomposition and explicit time allocation, limiting their scalability to highly geometrically complex scenes. This paper introduces the Orthogonal Trust Region Planning (Orth-TRP) framework, which parameterizes trajectories as the Cartesian product of orthogonal trust regions. Ellipsoidal safety corridors implicitly encode spatiotemporal constraints, eliminating the need for explicit time parametrization. By leveraging convex relaxation and separable block-wise constraints, Orth-TRP decouples problem dimensionality from environmental complexity, enabling parallel optimization. Evaluated on quadrotor benchmark tasks, Orth-TRP achieves significantly reduced computation time while generating smoother, safer trajectories—outperforming state-of-the-art corridor methods, especially in highly cluttered environments.

To address the slow generation and low reliability of convex sets in configuration space for real-time robotic motion planning under dynamic environments, this paper proposes the first GPU-accelerated online probabilistic collision-free convex decomposition method—Safe Convex Sets (SCS). Our approach enables efficient iterative refinement of SCS sequences via parallelized configuration-space inflation, joint SCS optimization, trajectory-guided collision-feedback pruning, and Dynamic Random Map (DRM) search. Furthermore, we integrate piecewise-linear path inflation with nonlinear trajectory optimization subject to convex-set constraints to support perception-closed-loop online planning. Evaluated on standard simulation benchmarks, our method achieves a 17.1× speedup over CPU-based baselines and improves collision-free success rate by 27.9%. Real-world experiments on a KUKA iiwa 7 robot demonstrate millisecond-level response times and high robustness in dynamic settings.

Time-optimal, collision-free trajectory planning in complex dynamic environments suffers from sensitivity to initialization and difficulty handling spatiotemporal coupling constraints. Method: This paper proposes a global optimization framework based on Spatio-Temporal Graph-of-Convex-Sets (ST-GCS). It systematically models diverse spatiotemporal constraints—e.g., obstacle avoidance, dynamic obstacles, timing bounds—as convex set constraints, eliminating dependence on initial guesses. By integrating graph neural network–guided structural modeling with efficient convex optimization, the framework enables consistent time-optimal trajectory generation across both static and dynamic scenarios. Results: Experiments demonstrate that the method reliably produces time-optimal, collision-free trajectories without requiring an initial guess. Its planning performance matches standard GCS while offering greater generality. Crucially, it significantly enhances ST-GCS’s capability to model intricate spatiotemporal constraints and improves solver robustness in dynamic environments.

This work addresses the problem of constructing Safe Flight Corridors (SFCs) for autonomous navigation, aiming to efficiently approximate free space while ensuring trajectory safety. The proposed method introduces an online iterative convex covering optimization framework that alternately optimizes partially distributed variables and incorporates geometric heuristics. It jointly generates overlapping polyhedral segments—subject to waypoint constraints—balancing maximal volume coverage with kinematically feasible initialization. Its key contribution lies in the organic integration of convex optimization, polyhedral geometric modeling, and constraint-satisfaction optimization, enabling real-time SFC reconstruction within a two-stage motion planning pipeline. Extensive evaluation across diverse parametric environments demonstrates significant improvements in trajectory feasibility and computational efficiency. The approach provides a scalable theoretical and practical foundation for online safe navigation in complex, dynamic scenarios.

Existing motion planning frameworks struggle to simultaneously ensure trajectory predictability, cross-platform consistency, and hardware deployability in industrial-grade safety-critical, high-repetition scenarios—such as robotic learning dataset construction and multi-robot coordination. To address this, we propose the first open-source motion planning framework specifically designed for multi-robot manipulation tasks. It integrates search-based algorithmic design, supports major simulators including MuJoCo, SAPIEN, and PyBullet, and provides dual Python/C++ APIs alongside a MoveIt! plugin for seamless hardware integration. Our framework achieves unprecedented reproducibility and cross-platform consistency in trajectory generation for multi-robot tasks. Extensive validation across diverse robot platforms demonstrates significant improvements in planning stability, inter-platform consistency, and deployment efficiency—thereby bridging a critical gap in reliable, safety-aware motion planning tools for real-world industrial applications.

This work addresses the computational inefficiency of motion planning for high-degree-of-freedom robots operating under dynamic constraints in complex environments. The authors propose a high-speed trajectory planning method grounded in differential flatness, which maps the dynamics into a flat output space to enable analytical, time-parameterized trajectory generation. By integrating SIMD-based parallel acceleration with a sampling-based planning framework, the approach achieves, for the first time, a general-purpose, highly accurate, and ultra-fast trajectory planner for differentially flat systems—including robotic arms, ground vehicles, and aerial robots. Experiments demonstrate that the method generates dynamically feasible trajectories in microseconds to milliseconds in both simulated and real-world cluttered dynamic environments, substantially improving planning efficiency while rigorously preserving dynamic feasibility and tracking accuracy.

This work addresses the challenge of inefficient motion planning and excessively large search spaces for nonholonomic mobile robots operating in complex structured environments. To this end, the authors propose a rectangular corridor graph representation based on deterministic free-space decomposition. By constructing a compact yet overlapping set of rectangular corridors, the method significantly reduces the search space while preserving path resolution completeness. Integrating efficient graph-based search with analytical trajectory generation, the framework enables near-time-optimal navigation that respects kinematic constraints. Extensive experiments on both large-scale simulations and physical robot platforms demonstrate the approach’s efficiency and practicality, and the implementation has been made publicly available.

This work addresses the limitations of conventional sampling-based motion planners, which are typically restricted to offline settings and struggle to handle motion uncertainties that lead to trajectory tracking errors. To overcome these challenges, the paper proposes a unified online replanning framework that continuously optimizes future control inputs during execution to enhance both trajectory quality and tracking accuracy. The approach uniquely integrates asymptotic optimality with real-time replanning by combining sampling-based planning, online state-space exploration, and control optimization, thereby enabling high-precision trajectory tracking for dynamical systems in uncertain environments. Extensive simulations and physical experiments demonstrate that the proposed method significantly outperforms existing baselines in terms of trajectory quality, tracking accuracy, and overall performance.

This work addresses the suboptimality of motion plans in robotics that arises from neglecting the non-Euclidean geometric structure of configuration spaces. To this end, we propose a sampling-based planning framework that operates directly on Riemannian manifolds. Our method efficiently approximates Riemannian geodesic distances using a third-order accurate midpoint scheme and, for the first time, integrates Riemannian natural gradients with first-order retraction operations into local path generation. This approach preserves geometric fidelity while ensuring scalability to high-dimensional systems. Experimental results demonstrate that our planner consistently produces trajectories with significantly lower cost—measured under the kinetic energy metric—than both Euclidean planners and conventional numerical geodesic solvers across diverse platforms, including a planar two-link arm, a 7-DoF Franka manipulator, and an SE(2) nonholonomic system.