Inverse Dynamics-Based Motion Control of a Fluid-Actuated Rolling Robot

Abstract

In this paper, the rest-to-rest motion planning problem of a fluid-actuated spherical robot is studied. The robot is driven by moving a spherical mass within a circular fluid-filled pipe fixed internally to the spherical shell. A mathematical model of the robot is established and two inverse dynamics-based feed-forward control methods are proposed. They parameterize the motion of the outer shell or the internal moving mass as weighted Beta functions. The feasibility of the proposed feed-forward control schemes is verified under simulations.

Singularity-Free Inverse Dynamics for Underactuated Systems with a Rotating Mass

“…The underactuated systems (1) with two degrees of freedom [1] have a great common, similar inertial matrix M(q), with certain underactuated spherical robots [4]- [7]. This inertial similarity help us to generalize our studying problem.…”

“…This arbitrary inertia tensor I c can be considered as either the lead of rotating pendulum [4], [5] (yellow pendulum in Fig. 2) or interacting fluid/gas inside pipes for the rotating spherical mass [7] (blue fluid/gas in Fig. 2).…”

“…Example 2 A rotating mass system with arbitrary inertial tensor is chosen in this example. This inertia tensor I c can be related to a rod that connects the mass to the center of the rolling body [4], [5] or an interacted water with the rotating mass in pipes [6], [7]. Thus, with a circular trajectory as the previous example, condition (18) is transformed to…”

“…In this study, we choose a 4th order Beta function [5], [7] to arrive the carrier θ(t) toward its desired final configurations θ des by…”

“…Later studies took place by following these coupling conditions [11], [12] for controlling the Pendubot [13] and Acrobat [3], [14]. The same problem was highlighted and control strategies are developed relative to this limitation for spherical robots [5], [7]. Also, because the spherical carrier requires consecutive rotations without any angular limitations, the singularities due to inertial coupling become more challenging to deal with.…”