Summary of content: In order to allow the electromagnetic shielding effectiveness automatic test device to follow a given path in the shielding room, an open-loop controlled two-wheel differential drive trolley was designed, its kinematics was analyzed, and the dual The arc fitting curve method enables the trolley to walk according to a given curve. It is verified by a large number of exercise experiments that using this method to control the trolley can ensure that the horizontal and longitudinal deviation of the trolley within 3 m of travel is less than 30 mm, which can meet the needs of the system. Finally, according to the experimental results, the applicable scope of the method and the idea of further reducing the error are given.
Keywords: differential drive; motion control; fixed path; curve walking
introduction
Automated Guided Vehicle (Automated Guided VehICle, AGV) is a mobile robot with a certain degree of intelligence that can work autonomously or semi-autonomously. It has a wide range of operations in modern logistics and warehousing, flexible manufacturing, military fields, and operations in dangerous environments. Application prospects.
Many scholars have conducted research on the guidance and control methods of automated guided vehicles. Most of them use encoders, gyroscopes, ranging sensors, etc. to perform pose detection and path tracking for robots, and then perform closed-loop control of the motion. Some special occasions with high requirements for electromagnetic interference or complicated surrounding environment have certain limitations.
The two-wheel differential drive trolley designed in this paper is used as the mobile platform of the electromagnetic shielding effectiveness automatic test device. Because the system requires high electromagnetic compatibility for the test device, and the test environment is relatively complicated due to the presence of a large number of tapered absorbing materials, waveguide windows, and waveguides in the shielding room, a differential drive wheeled car without sensors on the body is proposed. It has a structure and can perform curved motion within a certain accuracy range, and has a large application space in low-cost, high electromagnetic compatibility requirements and complex environments.
1 Design of trolley driving mode
The schematic diagram of several driving methods commonly used in two-wheel differential drive trolleys is shown in Figure 1. The rectangle with hatched lines in the figure represents the driving wheel controlled by the motor, and the small circle represents the omnidirectional free wheel or spherical wheel, which mainly serves as an auxiliary support. effect. Figure 1 (a) is a three-wheel differential drive, Figure 1 (b), Figure 1 (c) is a four-wheel differential drive with additional contact points. Figure 1(d) shows a six-wheel differential drive.
This design chooses option (c). The advantage of this option is that the trolley's radius of rotation can theoretically be from 0 to infinity, can rotate in place, and has good movement flexibility. At the same time, the four-wheel structure has a larger load-bearing capacity than the three-wheel structure. Good stability. The disadvantage is that due to the four-point landing, if the ground is not flat enough, the driving wheel may be raised, causing the car to fail to move normally. In order to ensure the reliable contact between the four wheels and the ground, a buffer mechanism is added to the front and rear support wheels.
The differential drive trolley is used as the mobile platform of the electromagnetic shielding effectiveness automatic test device. The test device has high requirements for the positioning accuracy of the trolley, but does not require high movement speed. The angular displacement of the stepping motor is proportional to the number of pulses, and the speed is proportional to the pulse frequency. It can quickly start, reverse, brake, and lock when stopped. Therefore, a stepping motor is used as the driving motor.
The output of the stepping motor is transmitted through the reducer, the output shaft of the reducer is connected to the driving wheel of the trolley through a coupling, and the trolley platform and the driving wheel are connected through a ball bearing. The stepping motor uses 42BY250C two-phase hybrid stepping motor, the rated static torque is 0.54 N·m, the matching driver is the SH-20403 stepping motor driver, and the reducer uses the PS40003 planetary gear reducer with a reduction ratio of 9 Device.
2 Kinematics analysis and modeling
Figure 2 is a schematic structural diagram of a two-wheel differential steering AGV (only two driving wheels are shown in the figure). O1, O2 are the wheel centers of the left and right driving wheels respectively, the wheel spacing O1O2 is 1, and C is the center of O1O2. xOy is the geodetic coordinate system, and V1, V2 and VC are the speeds of the left and right driving wheels and the center point C of the vehicle body respectively. Assuming that the coordinates of C in the geodetic coordinate system are (x, y), the attitude angle of the AGV is represented by the angle θ between the VC and the x axis (which is positive when counterclockwise is specified), and the vector (x, y, θ) is represented The pose of the AGV in the geodetic coordinate system xOy.
It can be seen from Figure 2 that Oc is the instantaneous center of the speed of the trolley, and the influence of lateral slip is ignored when moving at low speed. According to the knowledge of kinematics, the speed VC at point C is:
VC=(V1+V2)/2 (1)
Hypothesis The angular velocity of the car body is ω. The situation shown in Figure 2 is clockwise movement. Therefore:
According to the principle of rigid body translation, the movement of the car at any moment can be regarded as a rotation around the instantaneous center OC of the car body. The turning radius R is:
The three kinds of motion modes of the differential drive car are determined by the three relations between V1 and V2: 
From the above analysis, the differential drive car designed in the article is a global controllable system, which is controlled by two steps The motor inputs the pulse frequency and indirectly controls the linear velocity VC and angular velocity ω of the trolley. Theoretically, the trolley can move in any pose; at the same time, due to the constraints of the system, it is assumed that the car body and the ground are purely rolling during the kinematics model analysis. , And no sideways sliding.
3 Realization of curve walking
According to the kinematic analysis of the differential drive trolley, under normal working conditions, the trolley can move in a straight line or an arc. If the trolley is to move according to a given curve, consider using an arc to approximate the curve trajectory.
3.1 Calculation of the radius of curvature of the curve
In the formula: M is the steering coefficient. When the point on the curve is turned counterclockwise, M=+1; when it is turned clockwise, M=-1.
3.2 Double arc fitting curve
Given curve 
, in the process of fitting, in order to be as close to the given curve as possible, and the curve is smooth and tangent at the connection points of each segment, the double arc fitting method is selected here.
Select the list points on the theoretical curve according to the required accuracy, calculate the radius of curvature at each point, judge its unevenness according to its formula (6), and then fit the following two situations:
(1) Required fitting There is no inflection point in the curve segment.
According to formula (6), if the curvature radii at the two ends of the curve segment to be fitted are all with the same sign, it is considered that there is no inflection point in the curve segment, as shown in Figure 3.
According to the actual movement of the trolley, the following fitting requirements are put forward during the specific fitting:
①The fitting arc must pass through the list point;
②The arcs on both sides of the list point are smoothly tangent at the list point, and the slope of the tangent line is in the theoretical curve. The list points are equal;
③The two arcs between two adjacent list points are tangent at the intersection of the arc and the arc;
④The arc radius on both sides of the list point in the curve segment should be in the list as far as possible with the theoretical curve The radius of curvature at the point is close.
Take the list points A, B, C, ... on a given curve, and record their coordinates as (xA, yA), (xB, yB), (zC, yC), ..., there are:
according to formula (7) Calculate the normal slope angle θA, θB, θC,… at each list point. According to formula (6), the radius of curvature ρA, ρB, ρC,… can be obtained. From these two sets of data, the theoretical curve passing the list point can be calculated The coordinate value of each center of curvature.
For the curve segment AB, 
two arcs are used to fit the curve segment AB. 
The centers of the arcs are O1 and O2, and the radii are O1A and O2B, respectively. The coordinates of O1 and O2 are (X1, y1) and (x2, y2) respectively. In order to meet the first and second
requirements mentioned above, the relational expression should be satisfied: in order to meet the third requirement above, the following should be satisfied Relationship:
Simultaneous formulas (8) and (9) contain 4 unknowns x1, y1, x2, y2, but there are only 3 equations, so they cannot be solved. In order to meet the above requirement ④, x1 is used as the optimization variable, and (|ρA|-O1A)2+(|ρB|-O2B)2 is the objective function, so the double-arc fitting problem is transformed into using these three The equation is an optimization problem with equal constraints, so that the objective function (|ρA|-O1A)2+(|ρB|-O2B)2 tends to the minimum. The specific process is: take the x coordinate of the center of curvature of the theoretical curve through point A as the initial value of x1, apply the optimization algorithm to optimize x1, so that the objective function tends to be minimized, and finally get (x1, y1) and (x2, y2) It is the center coordinates of the best two arcs used to fit the curve segment.
(2) There is an inflection point in the curve segment to be fitted.
According to formula (6), the curvature radius of the theoretical curve at two adjacent nodes is different, which indicates that the curvature direction of the theoretical curve at these two points is opposite. When the curve appears inflection point, as shown in Figure 4.
In this case, you only need to change the third requirement to the following relational expression: the
same as the first case, the center coordinates of the fitted arc can be obtained by calculation.
4 Experiment and result analysis
In the experiment, set the given curve as y=100(x/500+sin(x/500)), the unit of x, y is mm, here set △x=100 cm, the car is from the origin Start moving, through multiple experiments, measure the movement of the trolley to a few fixed points, average the coordinates of these points, and approximate the experimental results, as shown in Figure 5.
In Figure 5, the upper curve is the theoretical curve, and the lower curve is the actual walking curve. It can be seen that the deviation between the actual trajectory and the theoretical curve does not exceed 30 mm during the traveling of the trolley. In actual use, it can basically meet the given error requirement within 30 mm.
Through experiments on different given curves, it is found that when the radius of curvature of the curve is less than 10 m and the rate of change of the curve is not drastic, the accuracy of the movement can be better guaranteed.
Since the rotation frequency of the wheel is generated by the single-chip microcomputer, V1 and V2 cannot be changed continuously, so when the radius of curvature of the curve is larger, the adjustment range of V1 and V2 is smaller, so the error will become larger. This error can be reduced by increasing the frequency of the single-chip crystal oscillator, but it cannot be eliminated. In actual situations, the crystal oscillator that meets the requirements can be selected according to the required maximum fitting arc radius and accuracy.
5 Conclusion
In this paper, according to the requirements of the mobile platform of the electromagnetic shielding room automatic test device, a differential drive car is designed, and the car's driving structure, kinematics model, curve walking algorithm, etc. are introduced. Finally, the curve movement is verified by experiments. The control system of the trolley is an open-loop control mode, which cannot automatically correct path deviations. However, due to the simple structure of the control system and the easy realization of the trolley structure, it has certain application prospects in the field of robots with fixed paths composed of straight lines, arcs and uncomplicated curves in some occasions with high requirements for electromagnetic interference.