Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments
<|reference_start|>Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments: We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically, and this data can be used to construct a local control barrier function (CBF) that models a local set that is safe for a period of time into the future. Then, we use a smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single barrier function that models an approximate union of the N most recently obtained local sets. This composite barrier function is used in a constrained quadratic optimization, which is solved in closed form to obtain a safe-and-optimal feedback control. We also apply the time-varying soft-maximum barrier function control to 2 robotic systems (nonholonomic ground robot with nonnegligible inertia, and quadrotor robot), where the objective is to navigate an a priori unknown environment safely and reach a target destination. In these applications, we present a simple approach to generate local CBFs from periodically obtained perception data.<|reference_end|>
@article{safari2024time-varying,
    title={Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and
  Dynamic Environments},
    author={Amirsaeid Safari, Jesse B. Hoagg},
    journal={arXiv preprint arXiv:2409.01458},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01458},
    primaryClass={cs.RO cs.SY eess.SY}
}