Analysis of the motion characteristics of Marine Mecanum transport platform

This paper analyzes the shortage of unmanned systems in the traditional operation mode from the operational requirement of future war to unmanned systems, and puts forward the ship Mecanum transport platform.


Introduction
In the future war, various types of military unmanned equipment will emerge in large numbers as the widespread application of the unmanned platforms. Due to the limited transportation space and narrow workplace channel in the ship deck transportation system, traditional wheeled transport equipment consists of ordinary wheels system and corresponding steering system, which has many disadvantages, such as large turning radius, low utilization rate of space, poor mobility and low transfer efficiency. These adverse factors have seriously affected the work efficiency of the ship's material security system. While the comprehensive motion technology based on the Mecanum wheel can effectively solve this problem. Omnidirectional devices applied this technology can generate 3-DOF omnidirectional motion in two-dimensional plane. The omnidirectional transport vehicle loaded by the Mecanum wheel can reach the target location along any path. There is no steering structure of the ordinary power vehicle, and there is no steering wheel, while the desired body movement can be achieved only by the handle operation, especially in the narrow or crowded situations, it still has a much better flexible movement characteristics than other tradition sports equipment. At the same time, this technology has also effectively solved the problem of the transportation of long material in narrow spaces. The schematic diagram is shown in Figure 1. Several parameters such as radius R, width b, roller length L, number of rollers N, offset angleαand coincidenceεare included in designing a complete Mecanum wheel. According to the geometry of the Mecanum wheel, the description of individual wheel's roller coordinates is shown in figure 2. In Figure 2, set the bottom plane's center O as the origin, wheel axis as the Z-axis, and establish the O-xyz system. Circle O is the theoretical circle, R is the radius and line AB is the roller axis, αis angle between z-axis and roller axis AB, which is the offset angle. Curve AB is the contact line between the normal rolling wheel and the ground, and it is also the theoretical bus bar for generating roller bodies. C is the ground point, γandβare the central angled of the projection of the curve AB and AC in surface O-xy. The width of wheel is b 2Rsin , point E at the line AB, CE⊥AB, the length of CE is δ , from figure2 we In O-xyz plane, the point-wise equation of sub-axis AB is (2.2) According to the I1on design principle, the envelope of the roller is a complete circle which satisfy the following： N γ 2 2π (2.3) If and only if the equal sign is used in Equation 2.1, the linear roller length reaches its minimum: We can refer to a pair of involute cylindrical gear continuous transmission conditions that ( is the gear coupling coincidence degree, is the allowable degree of coincidence of gear transmission, generally set to 1.4 ). In order to ensure smooth transmission, the length L of the roller in Mecanum wheel is in range of： Therefore, the coincidence degree of Mecanum can be presented as In conclusion, the structure parameters of Mecanum wheel are listed in Table 2

The Establishment of the Unmanned platform 3D structure
The unmanned platform motion actuator based on the Mecanum wheel is mainly composed of four Mecanum wheels, reducer, platform chassis and four DC motors. The four Mecanum wheels of the platform are respectively controlled by four motors and are mutually independent in the working process to achieve the various movement states of the platform. The simplified model is shown in Figure 4: The simplified model of Unmanned platform According to the characteristics of geometrical parameters of Mecanum wheel, from the consideration of torque and speed, a decelerator with a reduction ratio of 20 is designed. Based on the overall size requirements, design the unmanned platform chassis.

The Establishment of dynamic model of unmanned platform
As is shown in Figure 5, the origin of the platform is O 1 , O 1 -xy is an absolute Cartesian coordinate system, C 1 -xy is a relative Cartesian coordinate system, and The origin of the coordinate is the center C1 of the Mecanum wheel. V x is the horizontal speed of the platform while V y is the vertical speed. ω 0 is the angular speed around the point O 1 , ω 1 、ω 2 、ω 3 、ω 4 are the rotational speeds of the four Mecanum wheels. The point of the absolute motion that relative to the Cartesian coordinate system O 1 -xy is C 1 , while Relative to the Cartesian coordinate system C1-xy, C1 does relative motion, thus the relative movement between the two systems is called implicated motion.

Figure5 Plane view of the unmanned platform
In absolute motion, the speed of point C 1 in coordinate system O 1 -xy is The moving velocity of w1's center C 1 in C 1 -xy system is： (3.3) R (3.4) To sum up: Deduce from the (3.5) and (3.6)： 3 1 Form these parameter we can get the offset angleαof the roller is 45°. It can be concluded that: From the above model, it can be seen that changes in the magnitude and direction of ω 1 、ω 2 、ω 3 、ω 4 affect the direction and speed of the entire wheeled unmanned platform, which consequently achieve full-scale movement.

The Analysis of the motion state of unmanned platform
According to the above mathematical model, when the platform rotates in situ, that is, the speed in the horizontal and vertical directions is 0, while the angular velocity is not 0, the following can be obtained: (3.9) When the unmanned platform moves back and forth, that is, the horizontal direction and angular velocity is 0, and the vertical velocity is not 0, we can get: Similarly when the unmanned platform moves left and right, that is, the vertical speed and angular speed are 0, and the horizontal speed is not 0, then: When the unmanned platform reaches the left front 45° or the right front 45° motion, that means the angular velocity is 0, and the horizontal and vertical velocities are not 0, it can be concluded that: Reviewing the above, the four wheels of the unmanned platform based on the Mecanum wheel can carry out the movement in different directions, as shown in Figure 6:

Simulation of the Unmanned Platform Based on Adams
In this paper, we first use UG to simplify the entity model of the unmanned platform, and then import it into the Adams software for simulation. Before the simulation calculation, the parts without motion relations between each other become a rigid body, and remove the rigid body which doesn't participate in the movement and doesn't affect the simulation analysis result. Secondly, ignore the deformation and mechanical errors of the unmanned platform, although it is slightly different from the actual situation, it greatly reduces the computation and it can ensure the accuracy of the calculation.
In the process of simulation, each small roller adds rotation pairs around its axis of rotation, because there are 15 rollers, there are 15 rotation pairs. The Mecanum wheel has 1 rotation pair relative to the unmanned platform, so the total Mecanum wheel has 16 rotation pairs, and the whole platform adds 64 rotation pairs. In addition to adding constraints, we also need to add loads to the model. The loads that need to be added in this simulation are as follows: 1) Add velocity in four Mecanum wheels to simulate motor movements, 4 in total.
2) Add vertical down force to simulate gravity, 1 in total.
3) Apply contact force between various part of the platform, 60 in total.
Simulation of virtual prototype model is shown in Figure 7:

Analysis of the simulation results of unmanned platform
This paper analyzes the three motion states of the platform(respectively along x,y and z axis). Simulation duration of all three states is set to 3s, with 3000 in steps and ±360rpm of the rotation speed. According to the simulation parameters, the micro wheel rotates three times in total, and the simulation results are calculated under the condition of the Mecanum wheel touching the ground and the dynamic friction coefficient is u=0. 1 and u=0.4. (1) Unmanned platform moving around z axis As shown in Figure 8 and Figure 9, the Mecanum wheel resistance moment and the platform vibration curve of an unmanned platform moving around the z axis under different dynamic friction coefficients are as follows:  (1), (2), and (3), it can be seen that the same motion state and platform dynamic performance under different dynamic friction coefficients are approximately the same, and the dynamic resistance moment of the platform is always very large at the beginning, and after a period of time, the resistance torque tends to be stable; The amplitudes of the vibrations in all three motion states are not large, indicating that the small unmanned platform based on the Mecanum wheel has good stability in the motion process.
Compared with the traditional differential phasechange unmanned platform, the Mecanum wheel has the advantage of in-situ steering, and the dynamic resistance torque of the wheel is approximately the same as the vibration of the vehicle body and other movement states during the steering process, and there is no excessive peak or instability of the body, and it has good steering performance.

summary
This paper mainly studies the small unmanned platform's motion characteristics of marine Mecanum wheels, and analyzes and compares the motion characteristics in different motion states and different dynamic friction coefficients. Firstly, analyzing the operational requirements of the platform, and the unmanned platform based on the Mecanum wheel was determined as the research object according to the limited working space and narrow working environment; then the three-dimensional simplified model of the unmanned platform was established by using Adams simulation to get the change curve of the wheel resistance moment and platform vibration. And analyze the results to determine the advantages of the unmanned platform based on the Mecanum wheel on the ship's deck.