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  1. 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. 
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    Free, publicly-accessible full text available December 1, 2025
  2. Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety for the general class of control-affine systems. One of the main assumptions when taking this approach is the a priori knowledge of the barrier function itself, i.e., knowledge of the safe set. In the context of navigation through unknown environments where the locally safe set evolves with time, such knowledge does not exist. This manuscript focuses on the synthesis of a zeroing barrier function characterizing the safe set based on safe and unsafe sample measurements, e.g., from perception data in navigation applications. Prior work formulated a supervised machine learning algorithm whose solution guaranteed the construction of a zeroing barrier function with specific level-set properties. However, it did not explore the geometry of the neural network design used for the synthesis process. This manuscript describes the specific geometry of the neural network used for zeroing barrier function synthesis, and shows how the network provides the necessary representation for splitting the state space into safe and unsafe regions. 
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  3. 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. 
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  4. Real-time navigation in non-trivial environments by micro aerial vehicles (MAVs) predominantly relies on modelling the MAV with idealized geometry, such as a sphere. Simplified, conservative representations increase the likelihood of a planner failing to identify valid paths. That likelihood increases the more a robot's geometry differs from the idealized version. Few current approaches consider these situations; we are unaware of any that do so using perception space representations. This work introduces the egocan, a perception space obstacle representation using line-of-sight free space estimates, and 3D Gap, a perception space approach to gap finding for identifying goal-directed, collision-free directions of travel through 3D space. Both are integrated, with real-time considerations in mind, to define a local planner module of a hierarchical navigation system. The result is Aerial Local Planning in Perception Space (AeriaLPiPS). AeriaLPiPS is shown to be capable of safely navigating a MAV with non-idealized geometry through various environments, including those impassable by traditional real-time approaches. The open source implementation of this work is available at github.com/ivaROS/AeriaLPiPS. 
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  5. 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. 
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  6. The advent of deep learning has inspired research into end-to-end learning for a variety of problem domains in robotics. For navigation, the resulting methods may not have the generalization properties desired let alone match the performance of traditional methods. Instead of learning a navigation policy, we explore learning an adaptive policy in the parameter space of an existing navigation module. Having adaptive parameters provides the navigation module with a family of policies that can be dynamically reconfigured based on the local scene structure and addresses the common assertion in machine learning that engineered solutions are inflexible. Of the methods tested, reinforcement learning (RL) is shown to provide a significant performance boost to a modern navigation method through reduced sensitivity of its success rate to environmental clutter. The outcomes indicate that RL as a meta-policy learner, or dynamic parameter tuner, effectively robustifies algorithms sensitive to external, measurable nuisance factors. 
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  7. 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. 
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  8. Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance demands can be achieved for robotics applications. Prevailing use has assumed full knowledge of the safety barrier functions, however there are cases where the safe regions must be estimated online from sensor measurements. In these cases, the corresponding barrier function must be synthesized online. This paper describes a learning framework for estimating control barrier functions from sensor data. Doing so affords system operation in unknown state space regions without compromising safety. Here, a support vector machine classifier provides the barrier function specification as determined by sets of safe and unsafe states obtained from sensor measurements. Theoretical safety guarantees are provided. Experimental ROS-based simulation results for an omnidirectional robot equipped with LiDAR demonstrate safe operation. 
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  9. null (Ed.)
    The TEB hierarchical planner for real-time navigation through unknown environments is highly effective at balancing collision avoidance with goal directed motion. Designed over several years and publications, it implements a multi-trajectory optimization based synthesis method for identifying topologically distinct trajectory candidates through navigable space. Unfortunately, the underlying factor graph approach to the optimization problem induces a mismatch between grid-based representations and the optimization graph, which leads to several time and optimization inefficiencies. This paper explores the impact of using egocentric, perception space representations for the local planning map. Doing so alleviates many of the identified issues related to TEB and leads to a new method called egoTEB. Timing experiments and Monte Carlo evaluations in benchmark worlds quantify the benefits of egoTEB for navigation through uncertain environments. 
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