Advances in Hybrid Modular Climbing Robots: Design Principles and Refinement Strategies

This paper explores the design strategies for hybrid pole- or trunk-climbing robots, focusing on methods to inform design decisions and assess metrics such as adaptability and performance. A wheeled-grasping hybrid robot with modular, tendon-driven grasping arms and a wheeled drive system mounted on a turret was developed to climb columns of varying diameters. Here, the key innovation is the underactuated arms that can be adjusted to different column sizes by adding or removing modular linkages, though the robot also features capabilities like self-locking (the ability of the robot to stay on the column by friction without power), autonomous grasping, and rotation around the column axis. Mathematical models describe conditions for self-locking and vertical climbing. Experimental results demonstrate the robot's efficacy in climbing and self-locking, validating the proposed models and highlighting the potential for fully automated solutions in industrial applications. This work provides a comprehensive framework for evaluating and designing hybrid climbing robots, contributing to advancements in autonomous robotics for environments where climbing tall structures is critical.

Extended Koopman Models

We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the potential for fast, globally optimal control of nonlinear, nonconvex systems. The first generalization, Convex Koopman Models, uses convex rather than linear dynamics in the lifted space. The second, Extended Koopman Models, additionally introduces an invertible transformation of the control signal which contributes to the lifted convex dynamics. We describe a deep learning architecture for parameterizing these classes of models, and show experimentally that each significantly outperforms traditional Koopman models in trajectory prediction for two nonlinear, nonconvex dynamic systems.

Coarse-Grained Nonlinear System Identification

We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's memory regardless of the order at which the Volterra expansion is truncated; this is a superpolynomial reduction in the number of parameters as the order becomes large. This efficient parameterization is achieved by coarse-graining parts of the system dynamics that depend on the product of temporally distant input samples; this is conceptually similar to the coarse-graining that the fast multipole method uses to achieve $\mathcal{O}(n)$ simulation of n-body dynamics. Our efficient parameterization of nonlinear dynamics can be used for regularization, leading to Coarse-Grained Nonlinear System Identification, a technique which requires very little experimental data to identify accurate nonlinear dynamic models. We demonstrate the properties of this approach on a simple synthetic problem. We also demonstrate this approach experimentally, showing that it identifies an accurate model of the nonlinear voltage to luminosity dynamics of a tungsten filament with less than a second of experimental data.