Planning the yaw correction trajectory based on the motor current detection

Planning the yaw correction trajectory based on the
motor current detection
ying weiqiang (  laring@126.com )
 Zhejiang University https://orcid.org/0000-0003-1440-6186
cheng kuang
 Zhejiang University
Lingyan Zhang
 Zhejiang University
Cheng Yao
 Zhejiang University
Fangtian Ying
 Zhejiang University
Shijian Luo
 Zhejiang University

Research Article

Keywords: PID Control, Yaw Correction, Trajectory Planning

Posted Date: April 19th, 2022

DOI: https://doi.org/10.21203/rs.3.rs-1515061/v1

License:   This work is licensed under a Creative Commons Attribution 4.0 International License.
Read Full License

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  20         Planning the yaw correction trajectory based
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  22               on the motor current detection
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  25           Weiqiang Ying1 , Cheng Kuang1 , Lingyan Zhang1 , Cheng
  26                  Yao1 , Fangtian Ying1 and Shijian Luo1*
  27                  1 Zhejiang
  28                               University, Hangzhou, 310007, China.
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  31             *Corresponding author(s). E-mail(s): sjluo@zju.edu.cn;
  32         Contributing authors: laring@126.com; Kuangcheng001@yeah.net;
  33            zhangly@zju.edu.cn; yaoch@zju.edu.cn; yingft@zju.edu.cn;
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                                              Abstract
  37
  38           This paper describes distributed adaptive methods for solving the
  39           trajectory distortion control problem of intelligent lawnmowers. The
  40           strategy we have chosen is to use the association of motor current
  41           changes with changes in the movement patterns of the trajectory to
  42           try to modify the relationship between the fuzzy controller and the
  43           Proportional Integral Derivative(PID)controller based on traditional
               fuzzy PID control theory in order to Design a new low-cost con-
  44
               trol scheme that uses the differences between current detection and
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               linearized models as data feedback, interpolates these linear mod-
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               els with the Takagi-Sugeno(T-S)fuzzy method[1] to approximate the
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               entire non-linear model, and then the concept of parallel distributed
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               compensation(PDC)synthesizes a state feedback controller. A linear
  49           quadratic regulator(LQR)is used to stabilize the system and achieve the
  50           desired response. A PID fuzzy control method is then used to form
  51           the control of the intelligent lawnmower motor.This strategy uses data
  52           feedback obtained by monitoring the left and right motor current fluc-
  53           tuations, and it can be seen from the practical results that the proposed
  54           method is effective in obtaining an ideal linear path with good tracking
  55           behavior in various situations.And this paper uses the current moni-
  56           toring changes control method to determine whether the bias voltage
  57           tested and confirmed that the method can achieve stable path control.
  58
  59           Keywords: PID Control,Yaw Correction,Trajectory Planning
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12   2    WeiqiangY et al.
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14   1 Introduction
15
16   Mobile robots, due to their increasing use in various fields such as security
17   surveillance, home surveillance for health and entertainment, research and
18   education[2–4], are attracting increasing attention and advances in the past
19   decade due to their home services and applications.
20       Since the smart lawnmower can break the problem down into several more
21   manageable parts,these parts can be solved individually and then combined
22   to solve the overall problem. A complex nonlinear model can be broken down
23   into a set of locally linearized models and then interpolated to get the overall
24   system.This approach is called Multi-Model-Approach (MMA), also known as
25   T-S modeling[1].The interpolation of all individual models is carried out using
26   fuzzy logic.
27       Recently,the use and control of differences between current detection and
28
     linearization models as data feedback to enable intelligent lawnmowers to per-
29
     form certain tasks has attracted a great deal of interest from researchers in
30
31   related fields.If you compare the results of performing tasks without feed-
32   back with those with feedback,it becomes clear that the overall performance
33   is more efficient and secure with feedback.The smart lawnmower’s bias is a
34   combination of studying currents and syncing.It has received a lot of attention
35   from autonomous systems and control groups. Cooperative coordination can
36   be described as assigning the left and right motors to follow a predetermined
37   path of travel while receiving useful information through their sensors and
38   maintaining the prescribed direction. The path trajectory can be coordinates
39   that the intelligent lawnmower must follow, or a specified driving area within a
40   certain limit (see[5] and references therein). Dead reckoning has already been
41   extended to the case of a mobile robot moving on uneven terrain. It provides
42   information on positioning for mobile robots by directly calculating parameters
43   such as position, speed and orientation[6].
44       In [10], the author proposed a mechanism structure for the mobile robot
45   with the advantage of adaptability using hybrid modes with active wheels.
46
     There is a lot of research and literature on smart lawnmowers.B.Patra et al.
47
     from the Indian Institute of Engineering Science, Technology and Technology
48
49   examined in detail the problem of tracking a smart two-wheel drive lawnmower.
50   By studying the kinematics, dynamics and the linear feedback controller, some
51   basic, e.g. straight and semicircular trajectories (continuous and discontinu-
52   ous) were simulated. The real trajectories largely correspond to the simulation
53   results through experimental results, while the ideal path of the intelligent
54   mower also depends on the actuator[7], and various control techniques that
55   are applied to the model are briefly described. Dynamics modeling, simulation
56   and system identification are also examined in other publications. a simple
57   proportional-integral-summation controller is given in Jithu et al[8] for use.
58   Posture control techniques using an observer are described in Xu et al[9].
59       The proprietary sensors measure values within the system (robot) such
60   as battery power, wheel position, joint angle, motor speed, etc.These sensors
61   can be encoders, potentiometers, gyroscopes, compasses, etc. Huiwen Guo and
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12                                                             WeiqiangY et al.      3
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14   Xinyu Wu from the Shenzhen Institute of Advanced Technology of the Chinese
15   Academy of Sciences proposed a visual localization system that is important
16   for lawn map creation and area coverage. They used stable light compensa-
17   tion and aimed the camera mounted on the smart mower towards the ground
18   to extract and match feature points through pairs of frames to locate the
19   smart mower[10].Huiwen Guo and Xinyu Wu et al. used the MATLAB2010b
20   software in their computer for data processing and the program ran in the
21   MATLAB2010b environment. Experiments proved the feasibility of their posi-
22   tioning system, but the amount of data processed by the computer was large.
23
     Some of the main challenges are navigation and path planning, localization
24
     and obstacle avoidance.
25
26       The application of fuzzy theory to control systems is widespread in the
27   literature. Mobile robotics has been in development for many years, but for
28   location technology, technology remains a hot research topic for scientists.
29   While there are many different positioning methods and the sensors used, there
30   are two broad types of positioning - absolute and relative. Absolute positioning
31   relies on external sensors etc. to infer the position of the mobile robot directly
32   in the location map, while relative positioning techniques rely on the position
33   in the previous or initial moment to create the final projection[10]. Common
34   absolute positioning techniques include satellite positioning, ultrasonic posi-
35   tioning, bluetooth positioning, visual positioning, and UWB ultra-broadband
36   positioning. The most important relative positioning technique is dead reckon-
37   ing. Initially, some authors tried to represent nonlinear systems by piecewise
38   linear approximations[11] using local models and switching. A few years later,
39   Takagi et al.
40       Navigation is a fundamental problem in robotics and other important tech-
41
     nologies. Linear path control or linear control is an important topic in practical
42
     application and research. The relative position, posture and speed of an intel-
43
44   ligent lawnmower must be controlled to avoid sagging when the travel path
45   changes from the task demands. The most common route method is to use
46   a compass to determine if a distraction is occurring, but compass stability is
47   susceptible to environmental and magnetic influences. Leader-follower control
48   strategies have been widely explored, including various techniques such as PID
49   control methods[12], and a non-linear controller has been developed by com-
50   bining nested saturation with consensus control to achieve a smart lawnmower
51   that can safely track the direction of travel change in a targeted manner.
52       The mobile robot determines its path in real time in order to avoid
53   randomly moving obstacles[13]. Other intelligent algorithms that have been
54   studied by researchers that are used by mobile robots to navigate differ-
55   ent environments are DE (the Differential Evolution) algorithm[14, 15], HS
56   (the Harmony Search) algorithm[16], BA(the Bat-Algorithm)[17] and IWO
57   (Invasive Weed Optimization)[18]. To ensure accuracy in the localization,
58   sensors and an effective positioning system must be considered.Object posi-
59
     tioning [20], robotics and AR(augmented reality) tracking[19] are of interest
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     in recent literature. Each of these sensors is used in robots, mobile devices
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12   4     WeiqiangY et al.
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14   and navigation systems[20–22]. The only advantages of using these sensors
15   are to calculate the position and orientation of a device and/or object.
16   Magnetometer is another sensor that is used to calculate heading angle by
17   sensing the earth’s magnetic field. They are combined with pose determination
18   technologies[14],Other methods used to determine indoor localization include
19   Infrared, Wi-Fi, UWB(Ultra-Wideband), Bluetooth, Wide Local Area Net-
20   workWLAN (), fingerprinting etc.,[23–26]. However, these methods have their
21   shortcomings, so it is necessary to combine two or more schemes in order to
22   get accurate results. It does have the advantage of better performance in terms
23
     of accuracy, but it is more expensive and more complex to calculate[27].
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         In this post a full dynamic model is used and the difference between the
25
26   current detection and linearization models is used to get a linear model. The
27   difference between the obtained linear model and the actual nonlinear system
28   at a certain operating point is added to the linear system, and satisfactory
29   results are obtained by taking into account disturbances in the design of the
30   controller.
31
32   2 Test platform construction
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34   The robot system is conceived by placing it on a mobile platform(Figture1).
35   The author uses the self-made lawnmower system as a basis to test the theory.
36   Among the main components: 24V lithium battery, two DC motors, rack; one
37   STM32F103 main control, two current detection modules(INA250A4), Wi-Fi
38   module, through which the experimental platform is built to obtain current
39   data.
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49   Fig. 1 Main structure:two 35W motors,a 24V power supply,a control panel
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53   3 Methods
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55   The one-way drive wheels going uphill and downhill cause a change in current
56   and yaw of the mower at the same time, and there is a regular trend.Therefore,
57   there is a theoretical basis for compensating for the motor Hall data based on
58   the current fluctuation. However, it should also be noted that the following
59   derivation (Sections 3, 4, 5) greatly simplifies the actual situation and the
60   actual situation is much more complex than the theoretical derivation. The
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     main ones include the following:
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12                                                           WeiqiangY et al.      5
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14       (1) The motor power factor differs with different loads and is not a linear
15   number.
16       (2) Slope surfaces, in addition to the angle, length parameters influence
17   the course and are often accompanied by wheel slip, which can change the
18   coefficient of friction.
19       (3) The efficiency of the mower’s power transmission structure varies with
20   different power outputs.
21       (4) Duty cycle control motors whose real-time currents are high-frequency
22   changing data, which makes it difficult to acquire accurate RMS(Rate Mono-
23
     tonic Scheduling) values.
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28   Fig. 2 Flow chart for detecting current fluctuations
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30
31       For the above reasons, it is difficult to build an accurate mathematical
32   model between current change and yaw angle, so we use a fuzzy control scheme.
33   Using the current change value and the current change duration as inputs,
34   we create a two-dimensional fuzzy controller, obtain empirical data based on
35   several tests(Figture2), obtain effective control parameters and finally output
36   suitable Hall compensation data.
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38
39
     4 Theoretical background of intelligent lawn
40     mower control
41
42   A very important part of the path control of the intelligent mower is to control
43   the car so that it goes straight. It is common practice to set up a serial PID
44   control system for the left and right wheels, using heading angle as input and
45   motor Hall data as feedback, with the following control flow diagram(Figture3).
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     Fig. 3 Two-wheel mower PID control flow chart
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60       This solution makes it possible to control the mower so that it drives in a
61   straight line on flat grass. In complex terrain, such as However, for example,
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28   Fig. 4 Flow chart for PID control (with fuzzy controller compensation) of a two-wheeled
     lawn mower
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31   on uneven surfaces and slippery surfaces in the rain, the mower will yaw due
32   to the error between the Hall feedback data and the actual distance the wheels
33   have traveled at that time. In this case, an additional compensation scheme
34   must be added to the basic control scheme.
35       A common compensation option is to add additional sensors to the mower
36   to aid in course keeping. One of these is the addition of an electronic compass or
37   motion sensor that forms the EMU’s inertial navigation unit. Another option
38   is to add cameras based on machine vision, again with algorithms or mileage
39   and heading data. However, both approaches have certain limitations. One
40   of them is the increasing costs, including the cost of adding and upgrading
41   hardware, and the increasing R & D costs due to the difficulty of developing
42
     software algorithms. The second are the limitations of the use case; Electronic
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     compasses are sensitive to the environment and susceptible to magnetic field
44
45   interference, motion sensors usually need to be calibrated, and cameras have
46   an unstable image in outdoor sunlight[28, 29].
47       To address this problem, we tried to devise a new course hold control
48   scheme based on traditional fuzzy PID control theory by modifying the rela-
49   tionship between the fuzzy controller and the PID controller(Figture4). First
50   and foremost, a fuzzy controller is added to the above-mentioned serial level
51   PID controller loop for Hall data. This fuzzy controller takes the current fluc-
52   tuation of the mower’s drive wheel motor as input and outputs various Hall
53   compensation data for various amounts of current fluctuation(Figture4).
54
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     5 The effect of grassland terrain on mower
57     deflection
58
59   In grassy terrain, two wheels driving over a slope at the same time do not
60   cause yaw. It is above all the difference in gradient between the left and right
61   wheels when driving over the slope that causes the mower to deviate from its
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14   original direction of travel. This leads us to an analysis of the situation on an
15   uphill bike:
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29   Fig. 5 Schematic diagram of single wheel slope) of a two-wheeled lawn mower
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         As can be seen from the diagram(Figture5), the distance traveled by the
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33   two wheels is different and the difference determines the yaw angle since it is
34   a single wheel crossing the ramp.
35       There are the following relationships:
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37                                 ∆L = L1 ∗ (1 − cosΦ)                             (1)
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39                                        α = ∆L/R                                  (2)
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        The combination of the above two equations gives:
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44                                α = L1 ∗ (1 − cosΦ)/R                             (3)
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46       The vehicle’s yaw angle α, the length of the ramp L1, θ is the angle between
47   the ramp and the ground, and R is the wheelbase of two wheels of the vehicle.
48   According to formula (3), the longer the longer the slope length, the larger the
49   angle between the slope and the ground and the more likely it is that the car
50   will yaw.
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     6 The effect of grassy terrain on motor current
54   As mentioned above, the main influence on yaw in grassy terrain is the differ-
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     ence in slope between the two wheels, so here we analyze the influence of slope
56
     areas on the current of the drive wheel motors(Figture6).
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58      Since the speed of the trolley motor is controlled by a PID speed loop,
59   the speed can be adjusted in an instant, so it can be viewed as a constant
60   uphill speed. The engine output at this point is equal to gravity. There is the
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26   Fig. 6 Analysis of forces on drive wheels uphill
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     following relationship:
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31                             P =U ∗I ∗η =F ∗V =M ∗ω                             (4)
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34                                     Ff = m ∗ g ∗ cosΦ                          (5)
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36                                           F = Ff                               (6)
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     The combination of the above 3 equations gives:
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40                               I = m ∗ g ∗ v ∗ sinΦ/(U ∗ η)                     (7)
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42        Where: m is the mass of the trolley, v is the linear speed of the trolley
43   wheels, U is the motor drive voltage, I is the motor drive current, η the motor
44   efficiency and θ the angle. is between the slope and the ground. From the above
45   equation it can be concluded that: the larger the slope angle, the larger the
46   motor current; the longer the slope, the longer the duration of the high current.
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     7 Discusion
50   Before the effectiveness of the fuzzy control could be tested, a tool had to be
51   introduced that could localize the position of the trolley in real time and thus
52   visually monitor the trolley course offset. The wireless location system UWB
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     (accuracy ± 5cm) was chosen here.
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55
56   7.1 Experimental site set-up
57   This time several iterations of the experiment were used to count the effect of
58   the fuzzy control compensation. To ensure consistent conditions for multiple
59
     experiments, the experimental site was set up as follows(Figture7).
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12                                                               WeiqiangY et al.   9
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14      (1) Design the guide groove of the trolley at the starting position to ensure
15   that the trolley starts in the same direction every time, the road conditions
16   are the same after repeated experiments.
17      (2) Arrange and add the UWB-3D positioning system to the Trolley UWB
18   tags added, which can provide real-time feedback on the position of the trolley.
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28   Fig. 7 Scene photos
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32   7.2 Experimental data pre-processing
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34   The focus is on processing motor detection currents using PWM controlled
35   motors with high frequency vibration data for current values as shown in the
36   following figure(Figture8).
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52   Fig. 8 Real-time sampling of raw data from motor circuits
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55       The data vibrations are too large and too frequent to be used as input
56   data for fuzzy control, so preprocessing methods must be included. A current
57   maximum is used here instead of the real-time value of the circuit. This is
58   achieved by using a time window in the algorithm in which a maximum value
59   is taken within each window period, which ensures that the maximum value
60   of the current is taken when the window is larger than the current oscillation
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12   10      WeiqiangY et al.
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14   period. At the same time, the cycle time is as short as possible and yet in real
15   time.
16                                Ff = m ∗ g ∗ cosΦ                               (8)
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18                                           X
                                             n

19                                    It =         (It + 0.5 ∗ W )                              (9)
20                                           t=0
21      Imax current maximum,It current real time,It ,I(t 1) are time window val-
22   ues, 0.5*W is error value compensation. (Cycle-specific values) The current
23   data after processing with this method are as follows:
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     Fig. 9 Current data after pre-processing,(a) Current when the motor is idling,(b) Normal
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     plane driving current conditions, (c) current variation for simultaneous uphill driving, (d)(e)
38   current variation for non-simultaneous uphill driving
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40
41      The above diagrams(Figture9) show the motor current values after the
42   maximum value and the test conditions are wheel idling and real grass driving
43   with different applied resistances.The amplitude of the current data in the
44   graph is already very small and is very clearly reflected in the ramp resistance.It
45   can therefore be used as an input for the fuzzy control.
46
47   7.3 Experimental Analysis
48
49   The first set of experiments, (a)Trajectory orientation test without the fuzzy
50   controller. The trolley control algorithm does not include a fuzzy controller,
51   so the trolley starts along the guide slot, goes straight for a distance, passes a
52   small manually designed ramp, and then moves on to reach a position to reach
53   the end. The UWB position data of the entire process is recorded in real time,
54   that is the trajectory of the car.The above experiment was repeated 10 times,
55   and the trajectory data were obtained 10 times and plotted as follows.
56       (b) Trajectory orientation test with the addition of a fuzzy controller. The
57   fuzzy controller was added to the trolley control algorithm and the other condi-
58
     tions were exactly the same as in (a) experiment.The experiment was repeated
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     10 times and the trajectory data was obtained 10 times. The trajectory data
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61   without fuzzy control and the trajectory data with fuzzy control essentially lie
62   on a smooth surface.
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     Fig. 10 Experimentally identical trajectory data (a,b) without fuzzy controller(Group1),(c)
24   Trajectory data without fuzzy controller,(d) Trajectory data for adding fuzzy con-
25   trollers(Group2)
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28      The second series of tests(Figure10(c)(d)), the half bump test. In order to
29   avoid coincidence and also to better debug the fuzzy control parameters, the
30   experiment was repeated with a different ramp and the above experiment was
31   repeated.
32
33   7.4 Experimental results
34
35   From the above comparison tests it can be concluded that after adding the
36   fuzzy controller to compensate for the Hall data, a better course correction
37   effect is achieved.
38
39   8 CONCLUSION
40
41   In this paper, a one-sided control strategy for uneven road conditions is
42   designed. The novelty of our approach is to establish a physical relationship
43   between the differences between the left and right current sensing and lin-
44   earization models and then to use the fuzzy inference engine structure of the
45   incremental adaptive fuzzy PID optimizer which controller gains are achieved
46   through LQR optimization in order to stabilize the system and get the desired
47   response. The leader-follower method is then used to provide control for a pair
48
     of left and right motors. Different cases are tested to get the desired path.
49
     Regardless of the different definitions given, sensor fusion is the integration of
50
51   information from multiple sources in order to improve the accuracy and qual-
52   ity of the content, also with the aim of reducing costs. It is observed that the
53   new linearization method and the proposed fuzzy control give a good track-
54   ing response and the results obtained are actually tested to get good results,
55   allowing a new way of thinking for controlling the course stability of the path.
56   The shortcoming of this work is that the realistic conditions prevent the test
57   site from digging a pit and thus cannot be tested for concave surfaces, but sim-
58   ilar results can theoretically be derived from the test results on raised surfaces
59   and the next work plan has to be considered as test on concave surfaces.
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14   9 DECLARATIONS
15
16   9.1 Ethics approval and consent to participate
17
     Not applicable.
18
19
20   9.2 Conflict of interest
21   No potential conflict of interest was reported by the authors.
22
23
24   9.3 Dataset to be available
25   All data generated or analysed during this study are included in this published
26   article.
27
28
29   9.4 Consent for publication
30   Not applicable.
31
32
     9.5 Funding
33
34   Not applicable
35
36   9.6 Authors’ contributions
37
38   Weiqiang Ying analyzed and visualized the data and wrote the manuscript,
39   Cheng Kuang analyzed and interpreted the antenna data, Lingyan Zhang
40   collates data and writes the first draft, Cheng Yao analyzed the data, and
41   proofread and edited, Fangtian Ying analyzed the data, Shijian Luo proofread
42   and edited.All authors read and approved the final manuscript.
43
44   9.7 Acknowledge
45
46   The authors acknowledge Computer Aided Product Innovation Design Engi-
47   neering Centre, Ministry of Education, for providing some of the experimental
48   data and helpful discussion and suggestions.
49
50   9.8 Authors’ information
51
52   Weiqiang Ying, study in electrical and control engineering for the PhD at Zhe-
53   jiang University in 2019.and he joined the Ministry of Education of Computer
54   Aided Product Innovation Design Engineering Centre.His research interests
55   include sliding mode control,motion control,and signal processing.
56       Cheng Kuang,Engineer at the Computer Aided Product Innovation Design
57   Engineering Centre, Ministry of Education. Mainly engaged in research in the
58   field of information product design and human-computer interaction
59       Lingyan Zhang,Information Product Design, School of Software, Zhejiang
60   University. Mainly engaged in research in the field of information product
61
     design, human-computer interaction, children’s health and learning.
62
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12                                                          WeiqiangY et al.      13
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14       Cheng Yao,Instructor of Information Product Design, School of Software,
15   Zhejiang University. He is the deputy director of the Computer-Aided Product
16   Innovation Design Engineering Centre of the Ministry of Education and a
17   member of the International Computer Society (ACM). Mainly engaged in
18   research in information product design, technology design, human-computer
19   interaction, industrial design, digital art and design, etc.
20       Fantian Ying,Professor, Zhejiang University,Deputy Director of Zhejiang
21   Province Service Robot Key Laboratory,mainly engaged in research in the field
22   of industrial design and integrated product innovation design.
23
         Shijian Luo,Professor, Zhejiang University, Ph. Research interests in Indus-
24
     trial design, user experience and product innovation design, service design,
25
26   ergonomics and human-computer interaction design.
27
28   Appendix A              Relevant data and information
29
30   https://github.com/laringying88/Planning-the-yaw-correction-trajectory
31
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