Semi-globally exponential trajectory tracking for a class of spherical robots

Abstract

A spherical robot consists of an externally spherical rigid body rolling on a two-dimensional surface, actuated by an auxiliary mechanism. For a class of actuation mechanisms, we derive a controller for the geometric center of the sphere to asymptotically track any sufficiently smooth reference trajectory, with robustness to bounded, constant uncertainties in the inertial properties of the sphere and actuation mechanism, and to constant disturbance forces including, for example, from constant inclination of the rolling surface. The sphere and actuator are modeled as distinct systems, coupled by reaction forces. It is assumed that the actuator can provide three independent control torques, and that the actuator center of mass remains at a constant distance from the geometric center of the sphere. We show that a necessary and sufficient condition for such a controller to exist is that for any constant disturbance torque acting on the sphere there is a constant input such that the sphere and the actuator mechanism has a stable relative equilibrium. A geometric PID controller guarantees robust, semi-global, locally exponential stability for the position tracking error of the geometric center of the sphere, while ensuring that actuator velocities are bounded.

Center-point steering analysis of tracked omni-vehicles based on skid conditions

“…The typical layout types of tracked omni-vehicles and other tracked omni-robots are mainly rectangular (Mortensen Ernits et al, 2017;Zhang and Yang, 2018;Huang et al, 2014;Singh et al, 2017;Hua and Zhang, 2019; denoted Type I), hybrid (Yang et al, 2019a, b;Liu et al, 2018; denoted Type II), and centripetal layouts (Chen et al, 2002;Roh et al, 2013;Y. Zhang et al, , 2019Zhang, 2018;X.…”

“…It has unparalleled advantages in narrow areas requiring high speed and high mobility (Wang, 2018). With the exception of robots containing running mechanisms similar to universal wheels (caster wheels) (Cao, 2018;Clavien et al, 2018;Yang et al, 2018) and robots in the form of a single ball (Karavaev and Kilin, 2017;Madhushani et al, 2017), omnidirectional mobile robots are divided into wheeled and tracked omni-robots according to different running mechanisms.…”

“…The running mechanisms of tracked omni-robots (hereinafter referred to as the "tracked omni-mechanisms") mainly include the free-roller track (Chen et al, 2002), Vuton crawler (Roh et al, 2013), Mecanum wheel crawler (Mortensen Ernits et al, 2017;Guan and Yuan, 2019), omnidirectional mobile track (Zhang, 2017;Li et al, 2012;Xing et al, 2018;Ma et al, 2015), planar omnidirectional crawler mobile mechanism (Tadakuma et al, 2017;Takane et al, 2019;Yu et al, 2020), omni-crawler (Tadakuma et al, 2012(Tadakuma et al, , 2014, and other omnidirectional tracks. According to whether it has the ability of active movement in two noncollinear directions, the tracked omni-mechanism can be divided into two types: active tracked and semi-active tracked omni-mechanisms.…”

“…An active tracked omni-mechanism has problems such as a complex structure and poor load capacity. The semi-active tracked omni-mechanism has strong load capacity and a wide range of applications, and it is suitable for small robots (Roh et al, 2013;Zhang and Yang, 2018) and large machinery (Mortensen Ernits et al, 2017;Fang et al, 2020). From the perspective of the projection of the 512 Y. Fang et al: Center-point steering analysis of tracked omni-vehicles grounding section of the running mechanism, an omnidirectional mobile track is the more representative of a semi-active tracked omni-mechanism.…”

Feedback Regularization and Geometric PID Control for Robust Stabilization of a Planar Three-link Hybrid Bipedal Walking Model

“…In this section we will develop a nonlinear controller that will exponentially stabilize the output during the swing phase and show that this is sufficient to robustly achieve an asymptotically stable periodic gait under the Assumption 1. The controller is based on the notion of feedback regularization control plus intrinsic PID control introduced in [18], [19], [22].…”