A Review of Active Mechanical Driving Principles of Spherical Robots <s> Uni-Dimensional COAM <s> A spherical mobile robot, rolling on a plane with the help of two internal rotors and working on the principle of conservation of angular momentum has recently been fabricated in our group. The robot is a classic example of a nonholonomic system for which many existing algorithms do not easily apply. The objective is to study feasible path planning algorithms on this system. In this paper, we present the design details of the spherical robot fabricated along with the hardware used. We use Euler parameters which describe a unit quaternion for orientation of the robot and develop mathematical model to avoid singularity problem. We also prove controllability of the system in the quaternion space. <s> BIB001 </s> A Review of Active Mechanical Driving Principles of Spherical Robots <s> Uni-Dimensional COAM <s> Spherical robot is a special type of mobile robot which spherical structure offers special characteristic of motion, for example it has the capability to recover from collisions with static or mobile obstacles in the same area. In this paper the motion control of a kind of spherical robot based on conservation of angular momentum is discussed. Firstly, the dynamic model of a simplified version of this kind of spherical robot is built and analyzed with Lagrange equation, and its differential motion equation is obtained and the relation equation between the motion of the spherical robot and the motion of the rotor is deduced. Then, how to control the motion of internal rotor to realize expected motion of this kind of spherical robot is presented. Finally, with the parameters of a prototype of a spherical robot the motion control approach is verified by simulations with Matlab and ADAMS respectively. <s> BIB002 </s> A Review of Active Mechanical Driving Principles of Spherical Robots <s> Uni-Dimensional COAM <s> A path planning algorithm for a spherical mobile robot rolling on a plane is presented in this paper. The robot is actuated by two internal rotors that are fixed to the shafts of two motors. These are in turn mounted on the spherical shell in mutually orthogonal directions. The system is nonholonomic due to the nonintegrable nature of the rolling constraints. Further, the system cannot be converted into a chained form, and neither is it nilpotent nor differentially flat. So existing techniques of nonholonomic path planning cannot be applied directly to the system. The approach presented here uses simple geometrical notions and provides numerically efficient and intuitive solutions. We also present the dynamic model and derive motor torques for execution of the algorithm. Along the proposed paths, we achieve dynamic decoupling of the variables making the algorithm more suitable for practical applications. <s> BIB003
A UNI-Dimensional COAM design of this type is presented by Shu BIB002 . In this design, a variable speed rotor is used for a bob. However, this particular design utilizes the CMG bob in a different manner than a standard pendulum-type drive system does. The acceleration from spinning the CMG faster or slower will cause the shell to turn. Furthermore, if the CMG is already spinning at a high rate, maneuvering it up and down as if it were a bob will cause a precession torque that may achieve higher torques than a normal pendulum-based design (see Figure 18 ). This robot utilizes COAM in a one-dimensional manner, but has the ability to reorientate that dimension in order to control its movement. Figure 18 . Schematic of rotor-based bob presented by S. Guanghui BIB002 . V. Joshi presents a robot that is controlled by two pairs of diametrically opposed CMGs as shown in Figure 19 BIB003 BIB001 . A single motor controller controls each CMG pair. As a pair's angular velocity increases, the shell will rotate in the opposite direction in order to maintain the system's total angular momentum. Having a second pair inside the ball means the ball's movement has a second degree of freedom and can move in a true holonomic manner. The state space calculations for this type of robot are much more complicated than a simple barycenter offset design, but true holonomy can be achieved. This is categorized as a Uni-Directional COAM robot because it has two systems that utilize the laws of COAM, but each system only involves one spatial plane in its COAM dynamics. 