Omnidirectional wheel has two structures, the first is a mechanical wheel, the second is a continuous switch wheel. The difference is that the roller shaft of the second continuous switching wheel is perpendicular to the hub shaft, while the Angle between the roller shaft of the first mechanical wheel and the hub shaft is 45 degrees [2].

Usually three rounds of omnidirectional mobile platform is axis into 120˚ Angle, wheel omnidirectional mobile platform of three distribution in the same circle in the center of the wheel, the wheel axis pointing in the direction of the mobile platform center, in order to simplify the structure of the mobile platform design and reduce the use amount of building materials, the appearance of the design into an equilateral triangle, the structure of the model as shown in Figure 1.

Under the condition of the actual by many factors, such as environmental temperature, the surface is smooth and in the actual process of rolling, the contact points of the theory of cyclical change, the roll number under the action of the static friction force of the axial and radial deformation of overlap, lead to the wheel and the ground contact point height change constantly, may cause the

vibration of the body or skid [3] [4]. But in order to simplify the omnidirectional mobile platform kinematics mathematical model, we assume here that all three identical to turn center distance, the ground there is enough friction to make the movement when the mobile platform will not skid and very flat on the ground [4], three indicators fully consistent motor and wheels, and ignore the influence of inertia, the whole mobile platform can be simplified as shown in Figure 2.

The V a , V a , V c are respectively the rotation speed of A, B and C motors, ω as a platform overall rotation angular velocity omega, V x and V y are the macroscopic moving speed of the platform relative to the world coordinate system, L 0 is the vertical projection distance from the center of the platform to the center of the wheel, and is the included Angle between the wheel axis and the X axis. Assuming that the axial direction of Wheel A is 90˚, the velocity conversion matrix of the three wheels is calculated as follows [5]:

( V a V b V c ) = ( − 1 0 L 0 sin π 6 − cos π 6 L 0 sin π 6 cos π 6 L 0 ) ( V x V y ω ) (1)

After simplified operation, the velocity relationship of each wheel can be obtained as follows:

{ V a = − 1 2 V x + 3 2 V y + L 0 ω V b = − 1 2 V x − 3 2 V y + L 0 ω V c = V x + L 0 ω (2)

Power if moderators to main control system of power supply and motor drive power supply, the moving platform of choice is 15 V lithium-ion battery as a power source, main control board needs to be 3.3 V and 5 V power supply and the power needed is small, so in order to reduce power consumption, the Buck step-down circuit will power reduced to 7 V, and then LDO linear regulators are used to output 3.3 V and 5 V. Motor drive needs 12 V power supply and large power, so DC/DC switching power supply is used to power the drive and fuse is used as overload protection of the power system. See Figure 4.

As the core hub of the omnidirectional mobile platform, the master controller is STMicroelectronics’ ARM Cortex-M3 kernel chip with a maximum speed of 72 MHz. This series of MCU has 16 KB - 1 MB Flash, including: FSMC TIMER, SPI, IIC, USB, CAN, IIS, SDIO, ADC, DAC, RTC, DMA and many other peripherals and functions, with a high degree of integration. The main control board

is mainly distributed with OLED screen display interface, handle interface, serial port interface, PWM output, motor positive and negative rotation control interface and encoder input interface.

The input of PID controller is the error e ( t ) between the given output value r ( t ) and the actual output value y ( t ) , and the input error e ( t ) is calculated by the advance ratio example, integration and micro-division operation, and u ( t ) is output from the control pitch [6]. The control principle of PID is shown in Figure 5.

The input error can be expressed as:

e ( t ) = r ( t ) − y ( t )

The mathematical expression of PID algorithm in the time domain is:

u ( t ) = K p [ e ( t ) + 1 T ∫ 0 t   e ( t ) d t + K i d e ( t ) d t ]

K p , K i , K d : represent the proportion, integral and differential coefficients respectively.

Since digital controller is used for control here, a discrete PID algorithm formula needs to be obtained:

u ( k ) = u ( k − 1 ) + K p [ e ( k ) − e ( k − 1 ) ] + K i e ( k )     + K d [ e ( k ) − 2 e ( k − 1 ) + e ( k − 2 ) ]

u ( k ) : represents the output value at the first k sampling time;

u ( k − 1 ) : represents the output value at the first k − 1 sampling time;

e ( k ) : the error values of input and output at the current sampling time;

e ( k − 1 ) : the error value of input and output at the last sampling time.

The incremental photoelectric encoder is used to obtain the motor speed. It is A kind of sensor that USES the photoelectric effect principle to convert the physical quantities such as Angle, position and speed into electrical signals and output them. Moreover, it directly USES the photoelectric effect principle to output three groups of square wave pulse A, B and Z phases. The phase difference between A and B pulses is 90o, so the rotation direction can be easily determined, while the Z phase is one pulse per rotation for reference point positioning.