A Review of Active Mechanical Driving Principles of Spherical Robots <s> Double Pendulum <s> Mobile robots have been traditionally designed with wheels and few have explored designs with spherical exo-skeletons. A spherical mobile robot that offers to have a number of advantages, is proposed in the paper. The success of our design is contingent upon development of control strategies for reconfiguration of the sphere. We address the open-loop control problem and present two strategies for reconfiguration. The first strategy uses spherical triangles to bring the sphere to a desired position with a desired orientation. The second strategy uses a specific kinematic model and generates a trajectory comprising straight lines and circular arc segments. As compared to existing motion planners, our strategies require less computation and provide scope for easy implementation. <s> BIB001 </s> A Review of Active Mechanical Driving Principles of Spherical Robots <s> Double Pendulum <s> The paper deals with the motion of turning in place of a spherical robot for military reconnaissance and unknown environment exploration developed by us. The robot belongs to a nonholonomic and under-actuated system. The robot has 3 DOF and 2 inputs. The motion of turning in place can make a spherical robot with higher dexterity and environmental adaptability. The mathematical model of the turning motion is established by theory of moment of momentum. The relationship between the motion parameters is deduced, which is the basis of motion simulation and control system. Based on the analysis of mathematical model, a stick-slip principle is proposed for turning in place of the robot which is driven by double ballast masses. The stick-slip process is divided to three stages which are interpreted in theory. The principle is verified by numerical simulation and prototype experiment. The results confirm the effectiveness of the principle. The errors between theoretical analysis and experiment are analyzed at last. <s> BIB002 </s> A Review of Active Mechanical Driving Principles of Spherical Robots <s> Double Pendulum <s> This paper deals with the dynamics and motion control of a spherical robot designed for reconnaissance and unstructured hostile environment exploration. The robot in this paper has three DOFs and two inputs, of which the nature is a nonlinear and underactuated system with nonholonomic dynamic constraints. The improved construction of two pendulums offers novel motion principle of spherical robot, which is moving simultaneously actuated by both eccentric moment and inertial moment generated by the two pendulums. Meanwhile the mobility is enhanced when the robot behaves dynamically. The emphasis is placed on the linear motion and turning in place motion control. The dynamic model of linear motion is formulated on the basis of Lagrange equation, and a smooth trajectory planning method is proposed for linear motion. A feedback controller is constructed to ensure the accurate trajectory planning. Turning in place motion is an indispensable element of omni directional locomotion which can enhance the mobility of spherical robots. The dynamic model of turning in place motion is derived on the theory of moment of momentum, and a stick-slip principle is analyzed. The two motion control methods are validated by both simulations and prototype experiments. <s> BIB003 </s> A Review of Active Mechanical Driving Principles of Spherical Robots <s> Double Pendulum <s> This paper introduces a spherical robot, called KisBot II, with a new type of two-pendulum driving mechanism. A cross-shape frame is located horizontally in the center of the robot. The main axis of the frame is connected to the outer shell, and each pendulum is connected to the end of the other axis of the frame respectively. The main axis and pendulums can rotate 360 degrees inside the sphere orthogonally without interfering with each other, also the two pendulums can rotate identically or independent of each other. Due to this driving mechanism, KisBot II has various motion generation abilities, including a fast steering ability, turning ability in place and during travelling, and four(forward / backward / left / right) directional driving ability on the ground. Experiments for several motions verify the driving efficiency of the proposed spherical robot. <s> BIB004
Another novel concept proposed in recent literature is a drive system with two pendulums on the inside. B. Zhao proposes such a device with an elliptical shell. Paired with a double pendulum, this allows the robot to turn in place BIB002 BIB003 . Parameters such as speed and maximum incline are not optimized in this design because the research is focused mainly on proof of concept and path planning. Springs are added to the system to dampen impacts on the internal mechanisms when traversing rough terrain or large bumps. The literature presents the theory, which is verified by simulation, and is then demonstrated on a proof-of-concept physical prototype (Figure 8 ). The robot is able to turn in place by usage of the "Stick-Slip" principle. In the first stage (stick), each pendulum is rotated up to a horizontal position slowly, but in opposite directions. This will cause a shift in the equilibrium and the robot will want to turn, but because the pendulums are rotated up slowly, the shift in equilibrium is not large enough to overcome the static friction force holding the robot in place. In the next stage (slip), the pendulums are quickly forced down to their original vertical orientation. This also causes a shift in equilibrium, but the rapid movement is enough to overcome the static friction force causing the robot to slip and turn in place. Another type of dual pendulum design is seen in Kisbot II. Its predecessor, Kisbot I, was based on a single pendulum design and had adaptive legs allowing it to climb stairs (discussed below). Kisbot II overcomes the need for utilization of the stick-slip principle by allowing the internal mechanics to rotate about an axis perpendicular to the axis of pendulum movement BIB004 . The axes of rotation of Kisbot II are pictured below. The side view of Kisbot II is shown in Figure 9 (a), and the front view is shown in Figure 9 (b). The side view illustrates the ability of the pendulums to rotate independently of each other in either direction about the diameter of the robot. Theoretically, the stick-slip principle described by B. Zhao could also be used to turn the robot in place. However, by adding the extra degree of freedom shown in Figure 9 (b), the pendulums can rotate Kisbot II from left to right as well as from front to back, eliminating the need for the stick-slip principle. Figure 10 . Picture of Spherobot and its system of shifting masses BIB001 . Some teams have devised another method altogether for barycenter offset designs. By placing the bulk of materials in the center of robot, the energy required to spin the sphere is reduced. Shafts connect the center mass to the outer shell and weights are designed to traverse these shafts as shown in Figure 10 . By moving the weights up and down the shaft, the center of mass is changed and the ball begins to roll BIB001 . A few main differences separate this shifting mass design from the pendulum design. First, this design is holonomic. Regardless of its orientation, it can move in any direction. However, the controls are more complicated because the main processor must keep real time orientation data as well as distance data of all masses. Another downside to this design is that the internal weights traverse their respective shafts slowly, resulting in a slow moving robot. It also may have a hard time rolling downhill freely depending on state of the masses.