Reachability-Aware Time Scaling for Path Tracking

Offline reference trajectories for active target tracking are needed both for building multi-modal tracking datasets and for benchmarking online tracking planners under repeatable conditions. We present Track A star (TA star), an offline search-based trajectory planner that targets the visibility-aware target tracking objective on a discretized four-dimensional spatio-temporal grid (x, y, z, t). TA star combines a layered Directed Acyclic Graph (DAG) search with three engineering optimizations: cross-time obstacle distance caching against a Bounding Volume Hierarchy (BVH), per-layer beam pruning, and a configurable multi-ray visibility evaluator. TA star employs a beam-pruned heuristic search on this discrete graph to efficiently find high-quality tracking trajectories. While it trades strict theoretical optimality for practical scalability, our empirical results demonstrate robust, near-baseline visibility performance at a fraction of the computational cost. On a 1000-scenario stress test across eight CARLA Optimized maps, TA star converges on all scenarios and completes in 45 s using 32 workers; on a 248-scenario controlled comparison against an unoptimized priority-queue A star baseline (BinaryHeap implementation) under identical scenario inputs and a 5 x 10^6 expansion cap, TA star reduces mean planning time by 23.0x and worst-case planning time by 11.8x, while raising convergence from 56.9% to 100%. On the n=141 baseline-converged subset, TA star changes average visibility by only -0.15 percentage points (pp), with no scenario exceeding a 5 pp drop. We position TA star as a practical offline reference planner under these specific conditions, with limitations and failure cases discussed for environments such as Town07 dense vegetation.

Autonomous high-speed navigation through large, complex environments requires real-time generation of agile trajectories that are dynamically feasible, collision-free, and satisfy state or actuator constraints. Modern trajectory planning techniques primarily use numerical optimization, as they enable the systematic computation of high-quality, expressive trajectories that satisfy various constraints. However, stringent requirements on computation time and the risk of numerical instability can limit the use of optimization-based planners in safety-critical scenarios. This work presents an optimization-free planning framework called STITCHER that stitches short trajectory segments together with graph search to compute long-range, expressive, and near-optimal trajectories in real-time. STITCHER outperforms modern optimization-based planners through our innovative planning architecture and several algorithmic developments that make real-time planning possible. Extensive simulation testing is performed to analyze the algorithmic components that make up STITCHER, along with a thorough comparison with three state-of-the-art optimization planners. Simulation tests show that safe trajectories can be created within a few milliseconds for paths that span the entirety of two 50 m x 50 m environments. Hardware tests with a custom quadrotor verify that STITCHER can produce trackable paths in real-time while respecting nonconvex constraints, such as limits on tilt angle and motor forces, with flight speeds up to 63 km/h.

In this paper, we present an online method for converting an arbitrary geometric path, represented by a sequence of states, and generated by any planner (e.g., sampling-based planners such as RRT or PRM, search-based planners such as ARA*, etc.), into a kinematically feasible, jerk-limited trajectory. The method generates a sequence of quintic/quartic splines that can be discretized at a user-specified control rate and streamed to a low-level robot controller. Our approach enables real-time adaptation to environmental changes and can be re-invoked at any instant to generate a new trajectory from the robot's current state to a desired target state or sequence of states. Under a bounded-obstacle-velocity assumption, the method provides conditional stopping-safety guarantees over a finite time interval in dynamic environments, while allowing bounded geometric deviation from the original path. Kinematic constraints, including jerk limits, are explicitly considered. We validate the approach in a comparative simulation study against a competing method, demonstrating favorable behavior w.r.t. smoothness, computational time, and real-time performance, particularly with frequent target-state changes (up to 1 [kHz]). Real-robot experiments demonstrate applicability in real-world scenarios, including scenarios with a human as an obstacle.