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This paper extends the gap-based navigation technique Potential Gap with safety guarantees at the local planning level for a kinematic planar nonholonomic robot model, leading to Safer Gap . It relies on a subset of navigable free space from the robot to a gap, denoted the keyhole region. The region is defined by the union of the largest collision-free disc centered on the robot and a collision-free trapezoidal region directed through the gap. Safer Gap first generates Bézier-based collision-free paths within the keyhole regions. The keyhole region of the top scoring path is encoded by a shallow neural network-based zeroing barrier function (ZBF) synthesized in real-time. Nonlinear Model Predictive Control (NMPC) with Keyhole ZBF constraints and output tracking of the Bézier path, synthesizes a safe kinematically feasible trajectory. The Potential Gap projection operator serves as a last action to enforce safety if the NMPC optimization fails to converge to a solution within the prescribed time. Simulation and experimental validation of Safer Gap confirm its collision-free navigation properties.more » « lessFree, publicly-accessible full text available December 1, 2025
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Safe quadrupedal navigation through unknown environments is a challenging problem. This paper proposes a hierarchical vision-based planning framework (GPF-BG) integrating our previous Global Path Follower (GPF) navigation system and a gap-based local planner using Bézier curves, so called B ézier Gap (BG). This BG-based trajectory synthesis can generate smooth trajectories and guarantee safety for point-mass robots. With a gap analysis extension based on non-point, rectangular geometry, safety is guaranteed for an idealized quadrupedal motion model and significantly improved for an actual quadrupedal robot model. Stabilized perception space improves performance under oscillatory internal body motions that impact sensing. Simulation-based and real experiments under different benchmarking configurations test safe navigation performance. GPF-BG has the best safety outcomes across all experiments.more » « less
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This paper describes a hierarchical solution consisting of a multi-phase planner and a low-level safe controller to jointly solve the safe navigation problem in crowded, dynamic, and uncertain environments. The planner employs dynamic gap analysis and trajectory optimization to achieve collision avoidance with respect to the predicted trajectories of dynamic agents within the sensing and planning horizon and with robustness to agent uncertainty. To address uncertainty over the planning horizon and real-time safety, a fast reactive safe set algorithm (SSA) is adopted, which monitors and modifies the unsafe control during trajectory tracking. Compared to other existing methods, our approach offers theoretical guarantees of safety and achieves collision-free navigation with higher probability in uncertain environments, as demonstrated in scenarios with 20 and 50 dynamic agents.more » « less
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This paper explores the use of passive, stereo sensing for vision-based navigation. The traditional approach uses dense depth algorithms, which can be computationally costly or potentially inaccurate. These drawbacks compound when including the additional computational demands associated to the sensor fusion, collision checking, and path planning modules that interpret the dense depth measurements. These problems can be avoided through the use of the stixel representation, a compact and sparse visual representation for local free-space. When integrated into a Planning in Perception Space based hierarchical navigation framework, stixels permit fast and scalable navigation for different robot geometries. Computational studies quantify the processing performance and demonstrate the favorable scaling properties over comparable dense depth methods. Navigation benchmarking demonstrates more consistent performance across high and low performance compute hardware for PiPS-based stixel navigation versus traditional hierarchical navigation.more » « less