An Automatic Dynamics Generation Method for Reconfigurable Modular Robot

Abstract

A method of automatic dynamics generation for modular robots is presented on modular level. The robot's link parameters are got from the modules' parameters and the Assemble Incidence Matrix (AIM) describing the module types, assembled orientations and sequence of a given robot configuration. Adjoint matrices are adopted to describe the forward mapping of velocities, accelerations from frames on the (i-1) link to that of the ith link, as well as the dual adjoint matrices are taken to describe the backward mapping of moments and forces between frames on the i and the (i-1)th links. A mathematically consistent recursive approach for dynamics of modular robot is got from the Newton-Euler formula in Lie Group form.

Dynamic cellular actuator arrays and the expanded fingerprint method for dynamic modeling

“…The key concept is to introduce a matrix, named incidence matrix, to represent a complex topology of a multibody system. This graph-theoretic approach enables automatic generation of dynamic equations [16,17]. While these methods do generate the equations of motion for the dynamic systems of interest to the current work, they are highly general and generate redundant equations requiring careful manual selection of state variables, or cut-sets, to have physical meaning to the reduced escholon form required to systematically generate the equations of motion.…”

“…The approach is built to aid automation and simulation of the cell array actuators, allows for fast recalculation for different cell array topologies, and provides an intuitive base for future controls work on cell array actuators. The dynamics representing a given cell array actuator could be generated using Dymola, SimScape, GTM [16,17], or other computational methods based on base principles. The presented expanded fingerprint method allows the dynamics to be calculated with less human effort, less computational effort, and with greater speed, especially when comparing different topologies and cell dynamics.…”

“…d i q,n and F i n can be replaced by I n • d i q and I n • F i respectively, meaning the n'th row of the identity matrix multiplied by vector d i q or F i . These substitutions are shown in (17) and when used in (8) yeld an equation for d i q,n with solely linear algebra construction.…”