PHODCOS: Pythagorean Hodograph-based Differentiable Coordinate System

This paper presents PHODCOS, an algorithm that assigns a moving coordinate system to a given curve. The parametric functions underlying the coordinate system, i.e., the path function, the moving frame and its angular velocity, are exact -- approximation free -- differentiable, and sufficiently continuous. This allows for computing a coordinate system for highly nonlinear curves, while remaining compliant with autonomous navigation algorithms that require first and second order gradient information. In addition, the coordinate system obtained by PHODCOS is fully defined by a finite number of coefficients, which may then be used to compute additional geometric properties of the curve, such as arc-length, curvature, torsion, etc. Therefore, PHODCOS presents an appealing paradigm to enhance the geometrical awareness of existing guidance and navigation on-orbit spacecraft maneuvers. The PHODCOS algorithm is presented alongside an analysis of its error and approximation order, and thus, it is guaranteed that the obtained coordinate system matches the given curve within a desired tolerance. To demonstrate the applicability of the coordinate system resulting from PHODCOS, we present numerical examples in the Near Rectilinear Halo Orbit (NRHO) for the Lunar Gateway.

A Deep Learning Approach To Multi-Context Socially-Aware Navigation

We present a context classification pipeline to allow a robot to change its navigation strategy based on the observed social scenario. Socially-Aware Navigation considers social behavior in order to improve navigation around people. Most of the existing research uses different techniques to incorporate social norms into robot path planning for a single context. Methods that work for hallway behavior might not work for approaching people, and so on. We developed a high-level decision-making subsystem, a model-based context classifier, and a multi-objective optimization-based local planner to achieve socially-aware trajectories for autonomously sensed contexts. Using a context classification system, the robot can select social objectives that are later used by Pareto Concavity Elimination Transformation (PaCcET) based local planner to generate safe, comfortable, and socially-appropriate trajectories for its environment. This was tested and validated in multiple environments on a Pioneer mobile robot platform; results show that the robot was able to select and account for social objectives related to navigation autonomously.