A 3D dynamic model of a spherical wheeled self-balancing robot

Abstract

Mobility through balancing on spherical wheels has recently received some attention in the robotics literature. Unlike traditional wheeled platforms, the operation of such platforms depends heavily on understanding and working with system dynamics, which have so far been approximated with simple planar models and their decoupled extension to three dimensions. Unfortunately, such models cannot capture inherently spatial aspects of motion such as yaw motion arising from the wheel rolling motion or coupled inertial effects for fast maneuvers. In this paper, we describe a novel, fully-coupled 3D model for such spherical wheeled platforms and show that it not only captures relevant spatial aspects of motion, but also provides a basis for controllers better informed by system dynamics. We focus our evaluations to simulations with this model and use circular paths to reveal advantages of this model in dynamically rich situations. © 2012 IEEE

Time‐optimal trajectory generation and observer‐based hierarchical sliding mode control for ballbots with system constraints

“…Various methodologies have been proposed to devise controllers for ballbots, which can be broadly categorized into two general groups. The first group involves the construction of controllers based on linearized models, such as 2‐loop PI‐LQR controller, 1 two PD controllers, 2 LQR combined with feedforward, 3 LQR for linear feedback controllers in References 4,5, LMI‐based linear feedback controller, 6,7 LQR/MPC 8 . These methods have the advantage of well‐responding in low‐impact environments, simple models, and fast calculations based on linearized fixed matrices.…”

Design and Performance Evaluation of a Spherical Robot Assisted by High-Speed Rotating Flywheels for Self-Stabilization and Obstacle Surmounting

“…These robots have the advantage of being able to produce drive torques higher than pendulum designs (i.e., torque arms are greater than the sphere's radius) but the disadvantages of large internal energy and undesired precession torques. Other rolling robot designs applied unbalanced masses that can slide along radial spokes equispaced in angular orientation [23,-26]; articulated curved exoskeletons are used for the robot to roll and walk [27][28][29][30][31], using the tensegrity structure to morph body shapes and make use of internal force to move [32][33][34][35][36][37][38], spring loaded masses [7], magnetic fields [39,40], and even fans [41]. Several provide jumping capability [7,32,38,[42][43][44], some suggest impulsive rolling [28], while others combine gyroscopic forces and pendulums [45].…”