Geometric Controllability and Stabilization of Spherical Robot Dynamics

Abstract

Geometric control of a spherical robot rolling on a horizontal plane with three independent inertia disc actuators is considered in this note. The dynamic model of the spherical robot in the geometric framework is used to establish the strong accessibility and small-time local controllability properties. Smooth stabilizability to an equilibrium fails for the nonholonomic spherical robot. A novel contribution of this note is a smooth, asymptotically stabilizing geometric control law for position and reduced attitude, which corresponds to an equilibrium submanifold of dimension one. From Brockett's condition, this is the best possible dimension of a smoothly stabilized equilibrium submanifold. We also present a novel smooth global tracking controller for tracking position trajectories.Index Terms-Algebraic/geometric methods, stability of NL systems, robotics, spherical robot, position and attitude stabilization.

Stability and nonlinear controllability analysis of a quadrotor-like autonomous underwater vehicle considering variety of cases

“…Gui et al 16 proved a spacecraft-control moment gyro system is STLC. Muralidharan and Mahindrakar 17 proved that a spherical robot is STLC at the equilibrium using the Bianchini and Stefani's condition, 18 which is a particular case of the result proposed by Sussmann. 14 Liljeback et al 19 showed that a snake robot does not satisfy sufficient conditions for STLC.…”

Fractional-Order Adaptive Integral Hierarchical Sliding Mode Control Method for High-Speed Linear Motion of Spherical Robot

“…where ς is the viscous friction coefficient. According to the rolling friction couple moment model and the joint viscous friction model shown in (5) and 7, the expression of the controllable compensation torque τ fc is…”

“…Therefore, it cannot be effectively controlled by conventional motion control methods. At the same time, there are unmeasurable and unstable factors in the process of motion, such as incomplete dynamic model construction and unknown disturbances from the surrounding environment to the motion [4], [5]. With gradual increase of the motion speed, the influence of the above unstable factors on the motion control of the spherical robot increases rapidly.…”

Natural Walking Trajectory Generator for Humanoid Robot Based on Three-Mass LIPFM

“…The research and application of robots has been widely explored and discussed. The spherical robot [1], [2] and the wheeled robot [3], [4] are designed to facilitate the easy movement, and they are intrinsically stable robots, so they can be easily prevented from tipping over. However, these robots cannot move in some complex environments, such as stairs or uneven terrain.…”