Dynamic Modeling and Gait Analysis for Miniature Robots in the Absence of Foot Placement Control

Abstract

The study of animals and insects have led to realization that animals select their gaits, patterns of leg movement, according to speed. For proper gait planning, the legs must be controlled for proper foot placement with respect to the body motion and ground interactions. However, in small scale robotic platforms gait planning through foot placement control is neither cost effective nor easily attainable due to a lack of available sensors. Thus, even though a desired gait is envisioned at the design phase, it is not known whether the gait is optimum. In this work, we present the comprehensive dynamic model of the miniature foldable robot, MinIAQ-II, which has four independently actuated legs. Dynamic model is used to perform gait analysis, to investigate the difference between the intended gait and the achieved gait in the absence of foot placement control. The model is verified through slow speed walking experiments on flat terrain. The work presented can be modified for different miniature robots with passive legs to predict their locomotion under no foot placement control.

Control and study of bio-inspired quadrupedal gaits on an underactuated miniature robot

“…In previous robots, a common issue was that the legs were not perfectly parallel to the main body due to the material's flexibility and imperfect folding. However, in dynamic modeling, violation of the parallelity assumption can impact the simulation results [3]. To bridge this gap, we redesigned the leg assembly by adding custom 3D-printed motor housing, crank, and knee brace, to ensure that the legs remain in shape and parallel to the main frame.…”

“…In this simulation, a state vector of six translational and six rotational variables is solved at very small time steps using the dynamic equations and the stiff differential equation solvers in MATLAB. We then used the state vectors for visualization [3], so that it is easier to understand robot's locomotion.…”

“…The contact force model is an implicit function of all system states as well as the leg kinematics. Detailed derivation of the dynamics and the contact force model are presented in [3].…”

“…Although having various advantages, their small size comes with a price. Small-scale manufacturing techniques present limitations for their widespread use, and their limited power and lack of proper onboard sensing make controller design challenging [2,3]. Besides the control challenges, the size constraints and fabrication limitations often cause miniature robots to be designed with few actuators and fixed gaits.…”

Miniature Modular Legged Robot With Compliant Backbones

“…In order to investigate the effect of the number of legs and soft backbones on the miniature modular legged robot's locomotion, a comprehensive 3D dynamic model demonstrating the locomotion characteristics in smooth terrain is needed. A dynamic model for an n legged robot with compliant backbones is derived using the Newton-Euler formulation and the contact force model presented in [31]. Equations ( 5)-( 10) define the dynamics of the n legged miniature modular robot in three dimensional space.…”