arXiv subjects

Nathan Justus

Publications and source records attributed to Nathan Justus.

4 recordsLinked to original sources

arXiv2025

Geometric Data-Driven Multi-Jet Locomotion Inspired by Salps

Salps are marine animals consisting of chains of jellyfish-like units. Their efficient underwater locomotion by coordinating multi-jet propulsion has aroused great interest in robotics. This paper presents a geometric mechanics framework for salp-inspired robots. We study a new type of geometric mechanics models inspired by salps, in which control inputs are not restricted to the shape axes, analyze nonlinear controllability, and develop motion planning and feedback control methods. We introduce the "LandSalp" robot, which serves as a physical realization of the reduced-order, drag-dominated model of salp swimming, enabling controlled evaluation of locomotion strategies without many confounding factors of underwater experiments. We extend least-squares- and inverse-dynamics-based system identification to learn the Riemannian metric of the drag-dominated model from experimental data using Lie group differentiation. With about three minutes of data, we identify an accurate model of LandSalp. Simulation and hardware experiments demonstrate omnidirectional locomotion, shape regulation, and bending maneuvers, providing a principled pathway toward more capable salp-inspired robots.

cs.RO↗

arXiv2025

The Geometry of Optimal Gait Families for Steering Kinematic Locomoting Systems

Motion planning for locomotion systems typically requires translating high-level rigid-body tasks into low-level joint trajectories-a process that is straightforward for car-like robots with fixed, unbounded actuation inputs but more challenging for systems like snake robots, where the mapping depends on the current configuration and is constrained by joint limits. In this paper, we focus on generating continuous families of optimal gaits-collections of gaits parameterized by step size or steering rate-to enhance controllability and maneuverability. We uncover the underlying geometric structure of these optimal gait families and propose methods for constructing them using both global and local search strategies, where the local method and the global method compensate each other. The global search approach is robust to nonsmooth behavior, albeit yielding reduced-order solutions, while the local search provides higher accuracy but can be unstable near nonsmooth regions. To demonstrate our framework, we generate optimal gait families for viscous and perfect-fluid three-link swimmers. This work lays a foundation for integrating low-level joint controllers with higher-level motion planners in complex locomotion systems.

cs.RO↗

arXiv2021

Geometric analysis of gaits and optimal control for three-link kinematic swimmers

Many robotic systems locomote using gaits - periodic changes of internal shape, whose mechanical interaction with the robot's environment generate characteristic net displacements. Prominent examples with two shape variables are the low Reynolds number 3-link "Purcell swimmer" with inputs of 2 joint angles and the "ideal fluid" swimmer. Gait analysis of these systems allows for intelligent decisions to be made about the swimmer's locomotive properties, increasing the potential for robotic autonomy. In this work, we present comparative analysis of gait optimization using two different methods. The first method is variational approach of "Pontryagin's maximum principle" (PMP) from optimal control theory. We apply PMP for several variants of 3-link swimmers, with and without incorporation of bounds on joint angles. The second method is differential-geometric analysis of the gaits based on curvature (total Lie bracket) of the local connection for 3-link swimmers. Using optimized body-motion coordinates, contour plots of the curvature in shape space give visualization that enables identifying distance-optimal gaits as zero level sets. Combining and comparing results of the two methods enables better understanding of changes in existence, shape and topology of distance-optimal gait trajectories, depending on the swimmers' parameters.

cs.RO↗

arXiv2021

The Geometry of Optimal Gaits for Inertia-dominated Kinematic Systems

Isolated mechanical systems -- e.g., those floating in space, in free-fall, or on a frictionless surface -- are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers immersed in "perfect fluids" are able to use cyclic shape changes to both translate and rotate even if the swimmer-fluid system has no net linear or angular momentum. Finally, systems fully constrained by direct nonholonomic constraints (e.g., passive wheels) can push against these constraints to move through the world. Previous work has demonstrated that the net displacement induced by these shape changes corresponds to the amount of *constraint curvature* that the gaits enclose. To properly assess or optimize the utility of a gait, however, we must also consider the time or resources required to execute it: A gait that produces a small displacement per cycle, but that can be executed in a short time, may produce a faster average velocity than a gait that produces a large displacement per cycle, but takes much longer to complete a cycle at the same average instantaneous effort. In this paper, we consider two effort-based cost functions for assessing the costs associated with executing these cycles. For each of these cost functions, we demonstrate that fixing the average instantaneous cost to a unit value allows us to transform the effort costs into time-to-execute costs for any given gait cycle. We then illustrate how the interaction between the constraint curvature and these costs leads to characteristic geometries for optimal cycles, in which the gait trajectories resemble elastic hoops distended from within by internal pressures.

cond-mat.soft↗