Artificial intelligence control algorithm for steering motion of wheeled soccer robot

Abstract

In order to improve the function of driving of wheeled soccer robot and solve the time delay of the pivot steering motion of traditional robot, an artificial intelligent control algorithm for steering motion of wheeled soccer robot was proposed. Combined with the calculation of double eccentric steering motion control, the driving characteristic of wheeled soccer robot steering eccentric mass block was analyzed. Then, D’Alembert’s principle was used to analyze the stress of robot and design the kinematics model of spherical shell steering of spherical mobile robot. Moreover, the stick-slip principle was used to control the steering of wheeled soccer robot. Thus, the steering motion control of robot was achieved. Experiment results prove that the steering speed of wheeled soccer robot is 30% higher than that of traditional robot, which effectively solves the problem about the time delay of traditional robot steering motion.

Keywords

Wheeled soccer robot steering motion D’Alembert’s principle double eccentric mass

1 Introduction

Traditionally, micro-robot dynamics use the function relation between the torque of the micro motor and the size of wheel structure to complete the steering motion of robot. But, these algorithms are complex, which have the problem about the time–delay of steering motion. In order to improve the steering control effect of wheeled soccer robot, the kinesiology of micro robot is researched comprehensively. The torque consumption of micro motor is taken as the optimization target. The algorithm to control dual eccentric steering motion is used to design the wheel structure of micro robot wheel so as to solve the problem about steering time delay. Due to the special structure of micro robot, the method for solving and analyzing the kinematical constraint matrix rank is used to clarify its maneuverability and omni-directional characteristic, which provides a theoretical basis for the structure design and control of micro robot [4]. The sliding dynamics model of micro robot is built. Meanwhile, the simulation of sliding effect is performed based on the sliding dynamics model [11]. A sliding overcoming method based on visual feedback control is adopted to reduce the motion deviation [8]. The principle of micro-motor stepping location based on self-balance feature of torque is analyzed and the torque formula for the stepping drive of micro robot is derived. Based on the stick-slip theory, the dynamic algorithm of micro robot is established and the process of stepping motion is simulated [7]. This research shows that the torque of micro-motor has a great influence on the stepping stability. Therefore, the principle of stick-slip theory is used to realize the stable stepping and uniform step distance of micro robot. In addition, the kinematics equation of micro robot and the kinematic equation of micro-assembly arm are established respectively. Experiments show that the wheeled soccer robot based on stick-slip theory has the good driving ability.

2 Analysis of structure of driving unit of double eccentric mass block

When the robot collides or falls from heights, the current posture of robot is easy to be observed by the operator according to its contour. The ellipsoidal shell also limits the horizontal rolling of robot in a certain angle range. Thus, it cont not roll over when it traverses on the slope with a certain angle. The driving unit is the core of wheeled soccer robot. Most of the existing wheeled soccer robots use the driving mode of by eccentric mass block, and two vertical motors drive an eccentric mechanism, which control the forward and turning of robot. The robot moves flexibly, which can realize omni-directional motion [13]. But this driving mode also has obvious deficiency, the driving capacity of motor is not used to the maximum extent. Therefore, the maneuvering speed of robot is low and pivot steering ability is poor [5].

A drive unit with double eccentric mass block is designed. The driving unit is shown in Fig. 1. This system has two axisymmetric driving motors. Each motor drives an eccentric mass block. The mass block only can be rotated around the motor axis. Two mass blocks are symmetrically placed on the chief axis relative to the center of ball. Each eccentric mass is 350 g. The total mass accounts for 42.9% of robot mass. Compared with the traditional eccentric mass driving modes, this improved driving mode can provide the greater eccentric moment and inertia moment, which makes the robot faster and more flexible [20].

Fig. 1

Lateral view and overlook view of robot motion.

Figure 1 is the lateral view and the vertical view of robot movement. Mass m₁ and mass m₂ only rotate around the o axis. When the relative oscillation angle to the ground is respectively θ, θ₁ and θ₂, the barycenter of robot is at the intersection point o between MN and P. When the oscillation angle of mass block m₂ is θ and it is in reverse direction with θ₁, the barycenter of robot moves to the intersection o₂ between P and Q. Thus, the deflection angle of two mass changes the position of gravity center of robot, but it always moves on x axis, that is to say, no matter how the mass block yaws, the eccentric force of robot is always on F axis, and the eccentric moment revolves round F axis. The eccentric force can only make the robot roll around the axis, and cannot make the robot turn. The steering motion of robot depends on the inertia force. When the mass block and the spherical shell rotate quickly and relatively, the inertial force paralleling to y axis can be formed. The inertia force can be divided into the force along the axis m₁ and axis m₂ and the force couple around axis o₂. The inertia moment around x axis and y axis is formed along the component force of y axis and x axis, which can make the robot rotate around x axis and y axis [20]. The steering motion in situ is a special movement mode of wheeled soccer robot, which enables the robot to move in narrow space and enhance its adaptability for environment. The stress condition of steering motion of wheeled soccer robot based on double eccentric mass block drive is shown in Fig. 2.

Fig. 2

The force analysis of original steering motion.

3 Kinematic modeling of spherical shell steering for spherical mobile robot.

When the wheeled soccer robot moves on the horizontal plane, the motion of robot can be simplified as the “ball-plane” system (as shown in Fig. 3). In other words, (x, y, z) is the inertial coordinate system, xy plane is located on the motion plane [6]. That is to say, N, C, S are connected with the geometric center of spherical shell and they roll with the spherical shell, which is also known as the basic coordinate system of spherical shell. The coordinate origin C is located in the geometric center of spherical shell. It is assumed that there ia a homogeneous and symmetrical spherical shell, and the coordinate of spherical shell is (x, y, z) relative to the centroid C of inertial coordinate ψ. Three Eulerian angles in inertial space are the precessional angle p, the nutation angle e and the rotation angle w. When the axis YB is coincide and reverse with axis x, the precessional angle is equal to zero. The radius of spherical shell is φ. The inertial coordinate of contact point O between the spherical shell and the ground is (x, y, z).

Fig. 3

Coordinate system for free motion of isotropic symmetry spherical shells on horizontal plane.

Comprehensively, the design of driving mechanism of wheeled soccer mobile robot mainly use the gravity pendulum or approximate gravity pendulum to change the distribution of potential force field, so as to drive the spherical shell motion [17]. Because of the limitation of motion control technology, the above control methods of spherical mobile robot all use simple open-loop control, which indirectly control the output torque of motor and control the motion of spherical shell. Thus, the motion precision cannot be guaranteed [1 –3]. In the control of system, the motor controller based on DSP design is mainly adopted. But there is less research on the autonomous control system based on multi-sensor [16]. The wheeled soccer mobile robot has concise structure, which is much representative. But the control system that can carry many kinds of sensors and has independent motion ability is not successfully developed, which impedes the further application and development of wheeled soccer mobile robot [19]. Therefore, the problem about control system of spherical mobile robot needs to be further study. The steering motion of spherical mobile robot is nonlinear. The mature control method based on nonholonomic constraint kinematics equation cannot be directly applied to the kinematics control of spherical mobile robot [15].

During the steering motion, the robot makes pure rolling along the horizontal plane. Thus, its speed with contact point Q of plane must be zero. It is assumed that C is the velocity vector of geometrical center of spherical shell (center of sphere), and φ is the angular velocity vector of spherical shell, and φ is the radius vector from point N to point S, and z_b is the velocity vector at the contact point. Thus,

$\begin{matrix} Q_{n}^{0} = M (θ, ψ + \frac{π}{2}) F (z_{β} φ) \\ = [\begin{matrix} - C_{φ} P_{θ}, - C_{θ}, - S_{φ} P_{θ} \\ C_{θ} P_{ψ}, S_{φ}, P_{ψ} S_{θ}, S_{ψ} P_{θ} \\ - S_{θ}, - P_{ψ}, 0, C_{φ}, S_{θ} \end{matrix}] \end{matrix}$ (1)

If the pure rolling condition of spherical shell along the horizontal plane is $T_{n}^{0} = 0$ , the constraint equation of system motion is:

$\begin{matrix} F = {\hat{x}}_{β} (θ - C_{φ} P_{θ} \\ + S \hat{m_{1}}) + y_{β} [S_{ψ} + (- {MP}_{θ} - S_{φ} C_{ψ})] \end{matrix}$ (2) where, ${\hat{x}}_{β}$ and y_β are the motion equations with two inputs and five inputs respectively.

When the robot carries out a pure rolling motion on the horizontal plane, if the dynamics of driving mechanism are ignored, the system can be simplified as a homogeneous spherical shell motion with two inputs [9].

The steering plane of robot is situated in the rolling plane. E is the basic coordinate system of spherical shell. The original point of coordinate is located at the geometric center of spherical shell. When axis y is coincided and reversed with axis x, the spherical shell is located in the center of mass of inertial coordinate system E. The rotation of direction ${\hat{x}}_{β}$ and direction y_β are exerted on the spherical shell, and the mass distribution of spherical shells of robot as is shown in Fig. 4.

Fig. 4

Mass distribution of spherical shell of robot.

In actual applications, the mass distribution of spherical shell of wheeled soccer robot can be approximately uniform. Thus, we can assume that the center of mass is located at the geometric center [12]. Although the geometric center of frame is located at the center of sphere, the barycenter of frame deviates from the center of sphere after the various control devices are installed. When the robot moves along the longitudinal axis, the frame can rotate relative to the spherical shell. Meanwhile, the frame and the gravity pendulum are synchronized in the longitudinal direction [10]. Therefore, the centroid deviation of frame does not affect the motion of spherical shell relative to the center of sphere, that is to say, the motion of spherical shell is dynamic and stable. However, when the robot moves along the lateral direction, the frame and the spherical shell synchronously move in the lateral direction. The centroid deviation of frame relative to the center of sphere leads to the dynamic instability of spherical shell motion in the lateral direction [14].

When the micro robot is located on the micro-assembly system platform (two-dimensional plane), and it removes the focus from the chasis and put it on the clamp in the front of micro-assembly arm, the center of clamp can be located at any point on the plane and it has any angle [23]. Through above analysis, when the micro-assembly robot runs in the working environment, it has three free degrees. Thus, the micro-robot has the ability of omni-directional motion on the platform. In addition, the robot can redirect its wheels regularly and move along the new trajectory without changing its “footprints” [18]. In other words, when the micro-assembly robot changes the direction of motion, the turning radius is equal to zero. The coordinate of centroid of gravity pendulum in the inertial coordinate system is:

$\begin{matrix} [\begin{matrix} x \\ y \\ z \end{matrix}] & = [\begin{matrix} x_{β} \\ y_{β} \\ z_{β} \end{matrix}] + F_{y}^{x} S_{x}^{y} 〈 [\begin{matrix} l_{2} \\ 0 \\ 0 \end{matrix}] + P_{θ} [\begin{matrix} l_{i} \\ 0 \\ 0 \end{matrix}] 〉 \\ = [\begin{matrix} C, 0, P \\ 0, 1, 0 \\ - S, 0, C \end{matrix}] \end{matrix}$ (3)

By deriving the above formula, the velocity of the centroid of gravity pendulum to the inertial coordinate system is obtained. The algorithm is as follows.

$\begin{matrix} V = (P_{y}^{x}) S_{ψ} + x_{β} y_{β} {\dot{S}}_{φ}^{θ} \\ = (P_{y}^{x})^{m} ψ l^{i} + Sl (x_{β} M + {Fy}_{β}) \\ = l {[- ψ (C_{φ} P_{θ} + x_{β} y_{β}) - SPC]}^{i} \end{matrix}$ (4)

Although the simulation and experiment shows that the control strategy is effective, the control target controls the posture of spherical shell through the motion of gravity pendulum, and the dynamic balance control target controls the posture of gravity pendulum through the motion of spherical shell. Meanwhile, the rotary inertia of gravity pendulum is far greater than the rotary inertia of spherical shell. The use of double loop linear control strategy will increase the choice of control gain, which will exacerbate the dynamic performance. Thus, the double loop linear control strategy cannot be directly applied to the dynamic balance control of rolling inverted pendulum [21, 22]. Therefore, the simplified dynamic model is established and the double loop linear control strategy [24] is designed. To further study the characteristics of model and provide the reference for the dynamic balance system with similar structural feature, the partial linearization method is used to build the kinetic model of system, and a control strategy with global stability is designed. The longitudinal pitch motion of spherical mobile robot is taken as the reference, and the frame and the gravity pendulum are simplified as the homogenous connecting rod. The connecting rod can move around the center of ball under the action of rotational torque, which is the equivalent torque of longitudinal motor acting on the connecting rod through the reducer.

When the robot moves along the longitudinal direction, we only need to change the transverse posture of spherical shell so that we can change the direction of robot motion, which is determined by the Nonholonomic motion constraint and underactuation of spherical mobile robot. Therefore, lateral motion and longitudinal motion are the basis of motion control for spherical mobile robot. In conclusion, the motion mode of spherical mobile robot is proposed based on robot stability and convenience of online implementation. In actual application, a spherical mobile robot uses the desired motion path and kinematics model to design the path tracking method so as to determine the speed and direction of robot motion. Then, the motion speed and the motion pose of robot are controlled based on the longitudinal motion and the lateral motion. Thus, the analysis and design of the dynamic model and the control algorithm can be simplified. The process of longitudinal displacement is designed as shown in Fig. 5.

Fig. 5

Design of motion flow of longitudinal displacement.

Traditionally, the coupling action between the lateral movement and longitudinal movement of the robot are ignored, and the dynamic model and corresponding control strategy are established. Assuming that the spherical shell is completely symmetrical, if the horizontal coordinate axis of spherical shell is parallel to the ground, the trajectory of robot is a straight line. However, the actual model has error. In order to accurately evaluate the influence of strategy proposed in this section on the motion control performance of robot, a longitudinal displacement motion experiment is proposed. At the beginning, the frame of robot is parallel to the ground. During the movement, the lateral attitude control strategy is used to keep the lateral displacement. Meanwhile, the longitudinal motion control strategy is used to adjust the motion speed. In the control system, the position variable (x, y) of sphere center of robot is determined by the odometer method. The direction angle of robot is obtained by the inertial measurement device. When the robot reaches the destination and it is stable, we can obtain the position of sphere center by measuring reel. In practical application, the spherical mobile robot is affected by the environmental disturbance and the change of inertia parameter. The parameters of model are uncertain. The above control method may cause the deterioration or failure of control performance. Therefore, it is necessary to research the robustness motion control of spherical mobile robots based on uncertainty model. The simplified lateral motion dynamics model of spherical mobile robot is a control strategy of double loop linear motion, which is used to control the motion of spherical mobile robot and design the process of the lateral wheel soccer robot motion. The design result as is shown in Fig. 6.

Fig. 6

Design of motion flow of lateral wheeled soccer robot.

In Fig. 6, longitudinal angular velocity control and lateral attitude control strategy need to be designed based on dynamic model, which is the basis of controlling spherical mobile robot. Therefore, it is important to research the longitudinal angular velocity control and lateral attitude control of spherical mobile robot. The dynamic model of spherical shell ignores the coupling action among the gravity pendulum, the frame and the spherical shell. The multibody dynamic model is complex. The control strategy designed based on this model is not easy to be achieved on line. Then, the multi-body dynamic model of mobile robot is simplified. Thus, the dynamic model of the lateral motion and the longitudinal motion is obtained respectively. The dynamic model of longitudinal motion can be expressed as:

$P (θ, β) \bar{ψ} + m (φ, β) \ddot{β} + P (φ, x_{β}, y_{β}, ψ) = 0$ (5)

4 Steering control of wheeled soccer robot

The equivalent model of steering system of wheeled soccer robot is established on its mechanical feature and motion analysis. From the above design and analysis, the upper and lower disks connected by the connecting shaft with a slider are actually equivalent to a RP manipulator. Because the upper and lower discs are embedded in the upper and lower frame, the oscillating frame only has translational motion relative to the support frame. The oscillating frame is reverse rotation with the disk. The translational motion of legs of oscillating phase is perpendicular to the direction of guide rail. In order to simplify the analysis, we assume that the three legs have motion consistency, then resultant force acts on the centre line of rotary Table 1 of swinging phase. We assume that the mechanism is a rigid body model and the mass of connection axis is not considered. The steering system of this mechanism can be equivalent to a NCRP manipulator. Correspondingly, the equivalent relationship as is shown in Fig. 7.

Fig. 7

Equivalent mechanism of steering system.

Table 1

Kinetic parameters of model

Parameter classification	Parameter description	Parameter symbol
Model parameter	Supporting rail mass	M₁
	Oscillating guide rail mass	M₂
	Swinging leg mass	M₃
	Oscillating phase frame mass	M₄
	Inertia tensor of support rail 1	M₅
	Inertia tensor of support rail 2	M₆
Environmental parameter	Acceleration of gravity	L₁
	Horizontal included angle of rotation plane	L₂
	The angle between the rotating guide rail and the straight line L	L₃
	The distance between that cent of mass of the support guide rail and the rotate shaft	L₄
	Distance between center of mass of swing guide rail and axis of rotation	L₅
Seat parameter	Distance between center of mass of swing leg and axis of rotation	d₁
	The distance between that cent of the swinging turntable and the rotate shaft	d₂
	Distance between leg centroid and axis of rotation	d₃
	The distance between that cent of mass of the SW guide rail and the axis of the swing leg	d₄
	Up and down movement displacement of leg centroid	d₅

In Fig. 7, the guide rail 1 in the supporting phase rotates around the axis o which is perpendicular to its axis. The intersection point between the center line of guide axis and the axis center is o’. The straight line of the over o point in horizontal plane formed by its rotation which is parallel to the horizontal plane is o’, and the driving moment acting on the guide rail 1 is z, and the driving force acting on the guide rail and the leg is z, l, o”. The basic parameters of this manipulator, the pose parameters during motion and the environment parameters have directly relation.

Because the basic parameters of model are constant, the centroid of swing leg is coincided with the center line of swinging phase turntable, and the gravitational acceleration is constant. Thus, this dynamic equation of manipulator only contains four independent variables. Lagrangian dynamics method based on energy can be used to find the driving moment or driving force of each joint. The ADAMS software is used to establish the steering system model of omni-directional walking mechanism. The PID link is created based on the establishment of input and output link of control system. Matlab/Simulink is used to design the trajectory tracking control scheme of walking vehicle based on PID control algorithm. Meanwhile, the simulation of joint control is used for the motion tracking control of steering wheel. The steering tracking control system of robot as is shown in Fig. 8.

Fig. 8

Design of steering tracking control system of robot.

In the steering tracking control system of robot, it is necessary to design the combined control simulation method of system interface. The design method as is shown in Fig. 9.

Fig. 9

Simulation program of PID combined control system.

5 Simulation test and analysis

On indoor ground, the experimental research on the in-situ steering motion of wheel soccer robot based on double eccentric mass driven was carried out. The “in-situ steering” instruction was given to the robot by telecontroller. In the experiment, the input signal of mass block and parameter setting were consistent with the simulation, and the robot can complete the in-situ steering motion. At the starting moment of the mass block of in-situ steering motion of robot, the inertia moment produced the reverse angular velocity of robot due to the conservation of angular momentum. In other words, the steering direction of robot was opposite to the expected direction at the beginning of movement. But the reverse motion could be prevented by the ground friction moment in a short time. After the sliding stage, the rotational angular velocity of robot could not be reduced to zero at once. That is to say, the ground friction torque could not make the robot static immediately at the initial time of stagnation stage. The friction moment took 0.55 s to stop the robot motion. Therefore, the robot also had a small angular displacement at the stagnation stage. In addition to the in-situ steering motion, the robot also had periodic rolling motion. The rolling angular velocity was measured by sensor. The result was shown in Fig. 10.

Fig. 10

Detection of periodic rolling motion of robot.

According to above experiments, we could see that the in-situ steering motion of robot produced the inertia force with the same size and opposite direction through mass block. In the experiment, the synchronous motion of mass without error could not be guaranteed. Therefore, the inertia force along x axis produced imbalanced inertia moment around y axis, and the robot had the rolling motion. The eccentric mass block produced the maximum inertia force in the slip stage, and the robot had the maximum rolling angle speed in the sliding stage. The maximum value could reach 0.78 rad/s. In the stagnation stage, the rolling angular velocity gradually decreased due to the energy dissipation, which could not be reduced to zero in 0.8 s. Then, the robot moved to next sliding stage. In the process of in-situ steering motion, the robot had inevitable rolling motion. Therefore, the velocity of formal experimental method was 30% higher than the traditional method. According to the above kinematics equation, the simulation experiment was carried out. It was assumed the noumenon angle value was fixed. For convenience of observation, the steering deflection angle of wheel selected the fixed value. Thus, the velocity change rule of micro-gripper was the same as frequency of change of micro-motor. But, the amplitudes were different. The change rule of steering velocity of robot was more complex. In steering motion, the running velocity of robot was not only related to the velocity of steering motor, but also it was related to the rotation azimuth. Therefore, the experimental data only could be used to evaluate the dynamic performance of control process, which could not be used as a basis for evaluating the steady-state accuracy.

Figure 11 showed the corresponding curve that trajectory of rectilinear motion of micro-gripper changed with time, which coincided with the change rule of motion velocity. Moreover, after analyzing the relationship between the steering motion trajectory of robot and the angular displacement of micro-motor, we could see that the trajectory formed a ring, which also showed that the micro-gripper arm of robot had the ability of omnidirectional rotation. For repeated motion experiment of same target point, the average change curve of system state could be obtained through the mean processing for the measured values at the same time. In the experiment, the position change curve of spherical mobile robot was shown in the figure. Where, the solid line was the change curve of sphere center coordinate. The micro-robot could achieve 3600 steering without radius of gyration. In order to prevent the micro-motor signal line from being twisted, the steering range of micro-robot was limited between 700 and 900. Although the steering angle was artificially limited, the micro robot still moved along any direction in the plane. The distance deviation and angle deviation between the stop position and the theoretical target position were shown in Fig. 12.

Fig. 11

Detection of robot steering motion control.

Fig. 12

Distance deviation between stop position and theoretical target position in robot motion.

According to Fig. 12, the lateral slip velocity and friction resultant moment formed at both ends of curve were maximum, consequently the position offset and angle offset were also maximum. When the direction angle drew close to 450, the offset was gradually reduced. In the 450 position, the transverse slip velocity was also zero due to the zero force moment. Therefore, the micro robot did not generate angular deviation, but there was still a small position offset. Because acceleration and deceleration still caused longitudinal slip, the obvious slip was occurred during acceleration and deceleration of micro robot. During the uniform motion, there was little slip (very small, nearly zero). In conclusion, the position offset was caused by combined action of transverse sliding and longitudinal sliding, and the angular offset was caused by transverse sliding. Through three groups of sliding simulation researches, the following conclusions could be drawn: to simply change the motion direction angle could bring limited slipping effect. After considering the change of load-bearing ratio of wheel, the sliding amplitude began to increase, but it was not very large, and they had very regular offset curves. Meanwhile, most offset curves did not form the axis or center symmetry. Therefore, the dynamic process of wheeled soccer robot based on stick-slip principle was good. The robot in-situ steering control algorithm had higher control accuracy, which could effectively solve the problem about the time delay of traditional robot in-situ steering motion.

6 Conclusions

Compared with the traditional path planning method and the single reinforcement learning method, the mixed method can search an optimized motion path to improve the accuracy of micro-assembly operation of micro-robot. The proposed method has three effective measures: setting a buffer area, integrating into supervised learning and incentive system. It effectively prevents the robot from getting out of boundary while improving learning efficiency. In addition, three kinds of partition ways for state space of micro robot are designed. Under the same accuracy requirement, their learning efficiency increases in proper order. It shows that the effective partition of state space is very important. In order to improve the steering velocity of online path planning of robot, the knowledge base of path planning is established. Experimental results show that the pivot steering control algorithm of wheeled soccer robot based on stick-slip principle can effectively improve the steering speed of robot.

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