# Hybrid Locomotion Evaluation for a Novel Amphibious Spherical Robot
## The Amphibious Spherical Robot (ASR) III
### The Wheel Legged Water-Jet Composite Driving Mechanism  
As more multifunctional sensors are required when a robot increases in size and weight, the actuation mechanism becomes challenging. The robot diameter was 35 cm following a redesign to include more sensors. Buoyancy calculations indicated that the weight needed to be 11.22 kg before the robot sank in water. When standing, the four mechanical legs must support the robot and the numerous sensors; there is a danger that a sudden current surge might burn out the electronic  
Figure 1: The novel amphibious spherical robot III (ASR-III).  
circuit. Thus, we developed a wheel-legged and water-jet composite driving mechanism including the LSWM (Figure 2a) and mechanical legs (Figure 2b). The LSWM assists the robot to stand and perform on-land locomotion that is rapid on smooth, flat terrain. The mechanism reduces wear on the actuating mechanism (the steering gear, etc.), extending the working life of the robot. Also, the robot can slide down slopes, which saves a great deal of power.  
The LSWM is shown in Figure 2a. At the top, two servos can rotate through 360 degrees. The mechanism includes an upper support platform with four top beams and a lower support platform with four lower beams. A mobile platform with four supporting legs allows automatic transition between the sliding and walking modes. The ends of the legs bear four omni-directional wheels, allowing the robot to slide in any direction on flat, smooth terrain. As shown in Figure 2b, the mechanism also includes a mechanical leg with two joints, two servos, two omni-directional wheels, an upper holder, a lower holder, and a water-jet thruster. In previous work [36], the thruster was just used to spray water in one direction. Now, by the LM298N, a motor driving module, the thruster can spray the water in two directions. Therefore, for the forward motion and rotary motion in water, four water-jet thrusters all can be used simultaneously. The details are described in Section 3.  
When the robot moves from rough to smooth terrain, the two servos rotate in the same direction, simultaneously and synchronously, and the mobile platform drops vertically along the guide bar. Then, using the four mechanical legs, the robot switches to sliding locomotion. When the robot walks on rough terrain, the two servos rotate in the opposite direction simultaneously and synchronously, lifting the mobile vertically.  
The frequency of the control signal is 50 Hz, and the duty factor \(S_{PWM}\) of the pulse width modulation (PWM) signal can be set to obtain the desired angular velocity \(w\); the relationship is described by Equation (1).  
\[w=kS_{PWM} \tag{1}\]  
where, \(k\) is the scaling factor between the angular velocity and the duty factor of PWM signal.  
The LSWM is modeled using Equation (2).  
\[H=\Delta I\times\frac{n\times 2\pi}{kS_{PWM}} \tag{2}\]  
where \(H\) is the distance through which the support platform travels, \(\Delta I\) is the length travelled as the servo rotates once, \(n\) is the number of rotations, \(S_{PWM}\) is the PWM signal value, and \(k\) is as described above.  
Figure 2: The wheel-legged, water-jet composite driving mechanism. (**a**) The lifting and supporting wheel mechanism; (**b**) The mechanical leg of ASR-III.