Achieving Asymptotic Near-Optimality Without $δ$-Similarity

This paper introduces Bidirectional Tight Informed Trees (BTIT*), an asymptotically optimal kinodynamic sampling-based motion planning algorithm that integrates an anytime bidirectional heuristic search (Bi-HS) and ensures the meet-in-the-middle property (MMP) and optimality (MM-optimality). BTIT* is the first anytime MEET-style algorithm to utilize termination conditions that are efficient to evaluate and enable early termination on-the-fly in batch-wise sampling-based motion planning. Experiments show that BTIT* achieves strongly faster time-to-first-solution and improved convergence than representative non-lazy informed batch planners on two kinodynamic benchmarks: a 4D double-integrator model and a 10D linearized Quadrotor. The source code is available here.

This paper presents BOWConnect, a bidirectional parallel kinodynamic motion planner that addresses three fundamental limitations of existing sampling-based methods: sample inefficiency in high-dimensional state spaces, unreliable cost heuristics under dynamic constraints, and poor performance in narrow passage environments. Unlike classical planners that rely on random control sampling and geometric distance heuristics, BOWConnect integrates Bayesian Optimization over Windows (BOW) as a learning-based steering function within a parallel tree-based exploration framework, enabling each worker to learn local cost maps and constraints to guide sampling toward dynamically feasible and collision-free controls. A bidirectional architecture simultaneously grows forward and backward trees from the start and goal regions in parallel threads, with a spatial hashing mechanism enabling fast connection queries and a boundary value problem solver generating kinodynamically consistent bridge trajectories. Extensive evaluations across ten benchmark environments demonstrate that BOWConnect achieves 100% success while delivering the fastest or near-fastest planning time in complex scenarios, including narrow passages and non-convex spaces where state-of-the-art planners fail or degrade substantially. Real-world deployment on a ground vehicle and a quadrotor confirms real-time planning with no collisions. Videos of real-world and simulated experiments, high-resolution versions of the figures, and the open-source code are available at https://bow-connect.github.io/.

Sampling-based motion planners offer a practical and scalable approach to kinodynamic motion planning, notably for high-dimensional, underactuated, or non-holonomic systems. However, these planners are typically used offline, requiring execution to begin only after the trajectory has been computed. In addition, the planned trajectory may not be accurately tracked in the presence of motion uncertainty, leading to deviations from the nominal solution. In this work, these limitations were addressed within a unified framework, AURA, an asymptotically-optimal meta-planner framework that improves both path quality and tracking performance during execution. In addition to the main execution thread, this framework comprises a replanning method that continuously explores the state space and refines the trajectory during execution, and an optimization process that refines future control inputs to reduce tracking error. Together, these components enable AURA to leverage asymptotically optimal planning online while improving execution accuracy under motion uncertainty. The proposed approach is evaluated in both simulation and real-world environments across multiple systems, demonstrating consistent improvements in trajectory quality, tracking accuracy, and overall performance compared with baselines.