FORWARD MOVEMENT SYNCHRONIZATION OF TWO VEHICLES IN PARALLEL USING A LASER SCANNER K. H. Lee, R. Ehsani, J. K. Schueller ABSTRACT. A self‐propelled canopy shake and catch harvesting system is the most popular citrus harvesting machine in Florida and shows fruit removal of 95% and recovery of 90%. During harvesting, two machines work in pairs, one on each side of the row of citrus trees, necessitating synchronization of their forward movement. Unreliable synchronization causes inefficiency in the catching system which degrades the capability of the citrus harvesting system. Therefore, the overall goal of this study was to synchronize the forward movement of two test vehicles (master and slave) driving in a parallel path using a laser scanner. A control system, which consisted of a laser scanner, an electromechanical linear actuator, a data acquisition device , and a LabVIEW control program with an incorporated PID controller, was developed. The control system was mounted on a slave vehicle to synchronize its forward movement with that of the master vehicle. A PVC pipe was mounted vertically on the master as a target object for the laser scanner on the slave. The performance of the control system was tested in stationary and dynamic conditions. In the stationary test, distance errors measured using the laser scanner were between +0.31 and +0.37% for the distance range of 5.2 to 6.8 m (SD < 7 mm). At constant travel speeds in the dynamic test, maximum lead error, when the master was ahead of the slave, and maximum lag error, when the slave was ahead of the master, were 32 and 23 cm, respectively. Root‐mean‐square error (RMSE) was less than 10 cm. Using a trapezoidal speed change pattern, the maximum lead and lag errors were 17.3 and 10.9 cm, respectively. This control system demonstrated that it can synchronize forward movement of two test vehicles driving in a parallel path with an error of 11 to 32 cm at different travel speeds. Future work includes installing the control system on a mechanical harvesting machine and testing the performance under real citrus orchard conditions. Keywords. Laser scanner, Proportional‐integrative‐derivative (PID) controller, Speed control, Citrus.
T
he citrus industry in Florida is faced with the difficulties of labor shortages and increasing harvesting costs. Therefore, the citrus industry needs improved citrus mechanical harvesting systems that can compensate for the shortage of labor and reduce harvesting costs. Among different types of harvesting machines, a self‐propelled canopy shake and catch system is the most popular in Florida and shows fruit removal of 95% and recovery of 90%. The canopy shake and catch system consists of three main parts: a canopy shaking mechanism, a catch frame, and a fruit conveyor belt that are installed on a self‐propelled platform. The shaking mechanism consists of a series of rods that horizontally shake the tree canopy. This causes the fruit to fall down from the tree onto the catch frame. The harvested fruit is sent through a conveyor belt into
Submitted for review in November 2006 as manuscript number IET 6729; approved for publication by the Information & Electrical Technologies Division of ASABE in August 2007. The authors are Kyeong‐Hwan Lee, ASABE Member, Postdoctoral Fellow, Reza Ehsani, ASABE Member Engineer, Assistant Professor, Agricultural and Biological Engineering Department, University of Florida, IFAS, Citrus Research and Education Center, Lake Alfred, Florida; and John Kenneth Schueller, ASABE Member Engineer, Professor, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida. Corresponding author: Reza Ehsani, Agricultural and Biological Engineering Department, University of Florida, IFAS, Citrus Research and Education Center, 700 Experiment Station Rd., Lake Alfred, FL 33850; phone: 863‐956‐1151, ext. 1228; fax: 863‐956‐4631; e‐mail:
[email protected].
a truck, which transports the fruit to a trailer at the edge of the citrus orchard. The canopy shake and catch mechanical harvesting machines work in pairs, one on each side of the row of citrus trees, and usually one leads while the other follows (master and slave). The operation of the canopy shake and catch mechanical harvesting machines is a very stressful job. It involves conducting several simultaneous tasks, and one of them is to make sure the paired machines are synchronized to move side‐by‐side. The slave should neither lag nor lead the master. Currently, the operator of the slave machine makes a judgment of the leading distance between the master and slave and adjusts the travel speed based on the estimated distance. Therefore, accuracy of the synchronization is dependent on the operator's skill and experience. With a skillful operator, error in synchronizing forward movement of the paired harvesting machines in a citrus orchard is about ±50 cm, but many factors such as fatigue and citrus orchard conditions can affect this error. When the synchronization error increases, more fruit misses the catch frame and falls on the ground. To retrieve the additional fallen fruit, more labor and time is required. Therefore, automated and accurate forward movement synchronization of the paired harvesters improves the performance of machine harvesting as well as increases the productivity of the operator by reducing the number of tasks and stress levels. In synchronizing the movement of the paired machines, the first step is to measure the relative leading distance between the master and slave. For this, a laser scanner was
Applied Engineering in Agriculture Vol. 23(6): 827‐834
E 2007 American Society of Agricultural and Biological Engineers ISSN 0883-8542
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employed as a sensing device. Laser scanners are widely used in industry to detect objects for safety purposes or autonomous guidance. Their distance measurement is based on the time‐of‐flight principle. A single laser beam is emitted and reflected by an object's surface. The elapsed time between the emission and reception of the laser beam is used to measure a distance to the object. The laser scanner scans a fan‐shaped two‐dimensional measurement area by deflecting the laser beam using an internal rotating mirror. Numerous researchers have investigated the performance of laser scanners in detecting objects. Reina and Gonzalez (1997) tested the performance of a radial laser scanner with five different objects at different sampling rates and response times. The distance measurement using the laser scanner did not vary significantly with the color of the object, but did vary with the reflectivity of the object's surface. Also, the measured data were independent of the sampling rate and response time of the scanner. When a laser spot is located at the very edge of an object, the measured distance may be a combination of the foreground and background objects, that is, the measurement reading may fall in between the distances to the foreground and background objects. Ye and Borenstein (2002) called this measurement reading between the distances to the foreground and background objects a “mixed pixels condition” and investigated this condition by positioning an object at 1 m and a uniform background at 2 m. The mixed pixels condition was observed at the edges on the left and right hand sides of the object. Tsubota et al. (2004) designed an automatic guidance system for an autonomous tractor running in an orchard. A laser scanner was mounted on the tractor, facing toward the front. The distances to the trees on the sides of an alleyway in the orchard were measured sequentially in the range of the scanning angle. Using the Hough transform, the measured data were converted to virtual straight lines on each side of the alleyway. The tractor was guided to follow a center line between the straight lines on each side of the alleyway. Subramanian and Burks (2005) developed an autonomous steering system for a tractor traveling in a citrus orchard using laser radar and machine vision. The laser radar was used for both guidance and obstacle detection, while the machine vision was used only for guidance. The guidance system automatically guided the tractor through straight and curved paths. They reported that the performance of the guidance system using the laser radar was better than that using the machine vision. Kise et al. (2005) developed a laser scanner‐based obstacle detector that can detect a moving object and reconstruct a 2‐D silhouette of the object progressively in real time. They stated that accuracy in estimating the position, speed, and moving direction of the object relative to the tractor was sufficient for providing safety warning and collision avoidance for autonomous tractors in field operation. Martinez et al. (1998) developed a mobile robot that can follow a mobile object and avoid obstacles in its path using a laser scanner. The laser scanner measurement readings, distance to the object and heading angle, were used as input variables to the robot control system. Corresponding output variables of the control system were the new travel path and speed that could make the robot follow the mobile object, avoiding the obstacles in its way. White and Tomizuka (2001) built a control system for an autonomous following vehicle
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using a laser scanner. The laser scanner, mounted in the front of a following vehicle, measured the relative distance and heading angle between the preceding and following vehicles. The measured data were used in creating a trajectory for the following vehicle. OBJECTIVES The overall goal of this research was to synchronize forward movement of two vehicles (master and slave) driving in a parallel path using a laser scanner. The specific objectives were: S To test the feasibility of a laser scanner as a sensing device for measuring the relative leading distance between the master and slave, S To develop the hardware and software for controlling the travel speed of the slave, S To test the performance of the developed system in synchronizing the forward movement of the paired test vehicles.
MATERIALS AND METHODS EXPERIMENTAL SYSTEM The test vehicles equipped with experimental devices are shown in figure 1. A Ford 3000 tractor (master) and a Case DX23 tractor (slave) were equipped for test purposes. A laser scanner (model LMS200, SICK Inc., Germany) was mounted on a stand which was mounted on top of the slave vehicle's roll‐over protective structure at 2.6 m above the ground, facing a pole indicator mounted on the master vehicle. The laser scanner measured a position (direct distance and angle) of the master with respect to the slave by detecting a pole indicator on the master. A cylindrical‐shaped PVC pipe was chosen as the pole indicator because a cylinder provides a constant diameter at any field‐of‐view of the laser scanner. The pipe was painted white to maximize laser beam reflectance. The highest end of the vertical pipe was 3.2 m from the ground, and the outer diameter was 11.5 cm. The width of the object, which was in the field‐of‐view of the laser scanner, was checked to minimize the control error caused by recognizing an unexpected object as the pole indicator. Only when the width reading was close to the outer diameter of the pipe, the object was identified as the pole indicator.
5.0 m
3.2 m
Master
Slave 2.6 m
Figure 1. Test vehicles equipped with the experimental devices.
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The travel speed of the master tractor was measured using a GPS (model AgGPS132, Trimble Navigation Limited, Sunnyvale, Calif.) at a sampling frequency of 5 Hz, and then the speed information was transmitted via a wireless RS232 transceiver (model HPS‐120, HandyWave, Korea) to a notebook computer running at a CPU speed of 2 GHz on the slave (fig. 2). In the experiment, the GPS was used as a sensing device for travel speed measurement only and was not used in the synchronization control. A control program was written using LabVIEW (ver. 7.1, National Instruments Co., Austin, Tex.) to collect the relative position and travel speed data, process the data, and then to calculate the leading distance between the master and slave based on the collected position data. The obtained leading distance data were used as input to the proportional‐integrative‐derivative (PID) controller, which was incorporated into the LabVIEW program as a function provided by a LabVIEW PID control toolkit (ver. 6.0, National Instruments Co., Austin, Tex.). The input voltage for an actuator (model 722, ADDCO Inc., St. Paul, Minn.), which adjusted the position of a hydrostatic transmission (HST) foot pedal equipped on the slave tractor, was determined by the PID controller and was generated at an analog output port of a data acquisition device (model DAQPad‐6016, National Instruments Co., Austin, Tex.). Test Vehicles The travel speed of the Ford tractor master vehicle could be changed using a gear‐shift lever and a hand throttle. The position of the gear‐shift lever for forward movement ranged from 1 to 10. For the experiment, the gear was fixed at the position 5. Thus, the travel speed of the master was changed by adjusting only the position of the hand throttle. The travel speeds at the engine speeds of 800, 1000, 1200, and 1400 RPM were 0.66, 0.87, 1.04, and 1.30 m s‐1, respectively. Since the self‐propelled canopy shake mechanical harvester normally travels below 1 m s‐1 during harvesting, this speed range was considered appropriate to duplicate the travel conditions of the harvester in a citrus orchard. The DX 23 tractor equipped with a HST was chosen as the slave vehicle because the travel speed of the self‐propelled canopy shake mechanical harvester is controlled by a HST. The travel speed of the tractor can be determined by a hand throttle, a HST range selector lever, and a HST foot pedal.
The HST range selector has high and low speed ranges, and one neutral position. The travel speed of a HST vehicle is continuously variable from zero to full rated speed. For forward travel, the front pad on the pedal is depressed until a desired travel speed is reached; for reverse travel, the rear pad on the pedal is depressed. When the pedal is released, the transmission returns to neutral and the vehicle stops. For the experiment, the hand throttle was positioned at the engine speed of 1500 RPM, and the HST range selector lever was fixed at a high level. The travel speed of the slave was controlled only by the HST foot pedal. Laser Scanner The LMS200 laser scanner has two scanning range options: i) from 40° to 140° with the angular resolutions of 0.25°, 0.5°, and 1°, and ii) from 0° to 180° with the angular resolutions of 0.5° and 1°. Scanning times per cycle are 53, 26, and 13 ms at angular resolutions of 0.25°, 0.5°, and 1° in both scanning ranges, respectively. In this study, the LMS200 horizontally scanned the pole indicator in the range of 40° to 140° with the angular resolution of 0.25°. The laser scanner can communicate with a computer via a serial port at a baud rate of 9.6, 19.2, 38.4, and 500 kbps. In the experimental system, it was found that some of the data collected were occasionally lost when communication took place at 500 kbps via a PCMCIA high‐speed RS422 interface card (CSM GmbH, Filderstadt, Germany) while no data was lost at the slower speed of 38.4 kbps. Thus, for more reliable communication between the scanner and the computer, a 38.4‐kbps data transfer rate was chosen. The maximum measurement range of the LMS200 is 8 m with ±20‐mm system error in mm mode and 80 m with ±40‐mm system error in cm mode. For the experiment, the scanner ran in the mm mode. Actuator An electromechanical linear actuator, which is capable of holding a 14‐kgf load at a speed of 7.6 cm s‐1, was mounted underneath the driver seat of the slave tractor. The actuator uses a 12‐V DC brush‐type motor, which also drives an electromagnetic clutch inside the actuator. When power is applied to the clutch and motor, the actuator rod moves
Slave
Master
Computer
Pole indicator LMS
RS422 PCMCIA Serial Adapter
GPS
LabVIEW PID Controller
RS232 DAQ Wireless RS232 transceiver
Wireless RS232 transceiver
Analog Output
Actuator Foot Pedal
Figure 2. Functional block diagram of the experimental system.
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back and forth over its full stroke range and is held by the clutch. To drive the actuator rod to a given position, a DC voltage should be provided to a proportional electronic control module (ADDCO Inc., St. Paul, Minn.). The input voltage resolution for the movement of the actuator rod on an unchanged direction was 30‐mV DC. The actuator rod was connected to the rear pad of the HST foot pedal on the slave with a wire rope, which was guided on a pulley. When the rod was retracted, the front pad of the HST pedal was depressed, and the travel speed of the slave increased. The full stroke range of the actuator was 0 to 7.6 cm, and the input voltage ranged from 2 to 4.5 V. For the experiment, the stroke ranging from 0 to 4.5 cm was used, corresponding to an input voltage range of 2 to 3.5 V. The highest travel speed of the slave was achieved with the minimum stroke length, which corresponds to a 2‐V input voltage to the actuator. A sealed 10‐kohm feedback potentiometer inside the actuator provides a voltage signal to a proportional electronic control module (ECU). Using this signal, the ECM knows the position of the output rod at all times. The ECM compares the signal from the actuator potentiometer to the input voltage signal. If the signals do not match, the ECM provides 12 V DC to the actuator motor, which drives the output rod until the signals match. The 12‐V DC electromagnetic clutch in the actuator remains engaged under normal operating conditions. The clutch will disengage when power is removed as a result of intentional shutdown, electrical failure, or an error signal. PID Controller A control strategy based on a PID algorithm was selected because of its ability to handle vehicle dynamics without the requirement of developing a vehicle dynamic model. In PID control, a process variable and a setpoint should be specified. The process variable is the system parameter to be controlled, and the setpoint is the desired value for the parameter. In this study, the leading distance between the master and slave measured using the laser scanner was used as the process variable, and the setpoint was always set to zero. Hence, this was a regulator problem. A control error, e, was calculated by subtracting the setpoint value from the process variable value (eq. 1). A PID controller determines a controller output value, u(t), based on a proportional gain, Kp, an integral time, Ti, and a derivative time, Td: ⎛ 1 t de ⎞⎟ u (t ) = K p ⎢ e + ∫ edt + Td ⎢ T dt ⎟⎠ i 0 ⎝
(1)
The values of the three parameters (Kp, Ti, and Td) were determined using the rule proposed by Ziegler‐Nichols (Ogata, 1997). First, Ti and Td were set to R and 0, respectively. Kp increased from 0 to a critical value (Kcr) where the output first exhibits sustained oscillation. The critical gain (Kcr) and the corresponding period (Pcr) of the output oscillation were experimentally determined. The values of Kp, Ti, and Td were determined based on Kcr and Pcr using equations 2, 3, and 4, which were suggested by Ziegler‐Nichols in a normal control mode (LabVIEW, 2001). The output value of the PID controller was employed as the magnitude of the input voltage for the actuator to adjust the position of the HST on the slave.
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Kp = 0.25 Kcr
(2)
Ti = 0.5 Pcr
(3)
Td = 0.12 Pcr
(4)
Control Program A LabVIEW program was written to control the system and collect the direct distance data to the object from the laser scanner and the travel speed information of the master from the GPS. The program (fig. 3) established the communication setup and measurement mode for the laser scanner, and then started continuous data output from the scanner. The collected direct distance data were preprocessed. Only distances smaller than 7.9 m were saved with the measurement angle in a 2‐D data array. Time consumed for collecting the distance data and processing them was about 200 ms. Thus, the command to the travel speed control actuator based on the position determination was done at 5 Hz. Using equation 5, the width (W) of the object was obtained based on the distances (R1 and R2) and measurement angles (θ1 and θ2), which were the data saved in the first and last indexes of the data array in the LabVIEW program, respectively (fig. 4). W = R12 + R22 − 2 R1 R2 cos(θ 2 − θ1 )
(5)
The object was recognized as the pole indicator only when the width of the object was between 9 and 14 cm. The data in the second index of the data array were used as the direct distance and angle between the pole indicator and the laser scanner, that is, between the master and slave vehicles. Based on the measured direct distance (R) and angle (θ), an offset distance (D) and a leading distance (H) were obtained using equations 6 and 7 (fig. 5). The measured leading distance (H) data were used as the input of the PID controller. EXPERIMENTAL METHOD Experiments were conducted to test the measurement accuracy and repeatability of the laser scanner under stationary conditions and the performance of the control system under dynamic conditions. For the stationary test, the master vehicle was located at an angle (θ) of about 50° (fig. 5). The actuator on the slave was disengaged from the HST foot pedal to prevent the slave vehicle from moving. Therefore, the control program was used only to measure the direct distance and angle between the master and slave. An intended offset distance (D) between the master and slave was 5 m. The laser scanner on the slave measured a direct distance to the master for 1,000 readings. The test was repeated at angles of about 90° and 130°. The performance of the laser scanner in the stationary conditions was evaluated by the measurement error and standard deviation of the direct distance measured. For the dynamic test, two parallel straight lines with a length of 60 m and an offset distance of 3.8 m between them were made using yellow plastic ropes on an open, level field. The master and slave vehicles traveled along the left and right hand sidelines, respectively (fig. 1). The slave was steered by an operator, and the travel speed was adjusted by the control system. The offset distance between the pole indicator on the
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Pole indicator W
START
Setup communication andmeasurement mode for the laser scanner
R2 R1
Measurement angle = 40°
q1
q2
Measure direct distance at the angle
Laser scanner
Figure 4. Geometry for measuring the diameter of the pole indicator. Measured direct distance < 7.9 m
N
Master
Y
Moving direction
Save distance and angle data in a 2-D array
Measurement angle = Measurement angle + 0.25°
H
R q Slave
D Y
Measurement angle < 140°
N N
9 cm < wudth of object < 14 cm Y
Figure 5. Geometry for measuring a leading distance and an offset distance.
D = R · cos(90° - q)
(6)
H = R · sin(90° - q)
(7)
Calculate offset distance and leading distance
RMSE = PID Controller
ei2 i =1 N N
∑
(8)
where, ei is the error and N is the total number of data. Generate input voltage for the actuator
RESULTS AND DISCUSSION N
Stop ? Y STOP
Figure 3. Flow chart of the control program.
master and the laser scanner on the slave was maintained at 5 m by making a right‐rear tire of the master and a left‐rear tire of the slave follow the ropes on the left and right hand sidelines, respectively. The offset distance was determined based on the offset distance between the paired harvesters working in a citrus orchard and the space between the tree rows. The master traveled at four constant speeds of 0.66, 0.87, 1.04 and 1.30 m s‐1, and a trapezoidal speed pattern with a minimum speed of 0.64 m s‐1 and a maximum speed of 1.14 m s‐1. The travel speed of the slave was adjusted by the laser scanner‐based control system to keep detecting the pole indicator on the master at an angle (q) of 90°. The synchronization performance in the dynamic conditions was evaluated using maximum lead error (master ahead of slave), maximum lag error (master behind of slave), and root‐mean‐square error (RMSE) according to (eq. 8):
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TUNING THE PID CONTROLLER To determine the parameter values (Kp, Ti, and Td) of the PID controller, experiments were conducted at the four travel speeds in the dynamic test condition. When Ti and Td were set to R and 0, respectively, Kp increased from 0 to a critical value (Kcr), which generates first sustained error oscillation. The critical gain (Kcr) was 0.4 at all travel speeds. The corresponding averaged period (Pcr) of the error oscillation was 4.5 s (fig. 6). The proportional gain, integral time, and derivative time obtained using equations 2, 3, and 4 were 0.1, 2.25, and 0.54 s, respectively. These values were also applied for a dynamic test conducted with a trapezoidal speed pattern. The leading distance between the master and slave was used as the control error. STATIONARY TEST Direct distance and angle measurements in a stationary test at 90° are shown in figure 7. The measured distance data fluctuated even though the pole indicator and the laser scanner were fixed with a specific distance at a relative angle (q) of 90°. Most of the distance data were within ±10 mm from an averaged distance. Maximum distance was 21 mm greater than the averaged distance; minimum distance was 18 mm smaller. For 1,000 readings, the pole was always
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528
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20
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120 110
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20 250
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Figure 6. Control error in the test for tuning the PID controller with the critical gain of 0.4 at the travel speed of 0.87 m s‐1. Pcr is the period of the error oscillation.
Figure 7. Direct distance and angle measurement in the stationary test at 90.255.
detected at only one angle of 90.25°. Direct distance and angle data observed at 50° and 130° presented similar patterns with those shown in figure 7. True distance measurement between the pole indicator and the laser scanner was tried with a measuring tape. However, variation in the measurement using the tape was larger than that using the laser scanner. The distance measurement can be inaccurate due to the horizontal location of a reference spot, which a laser beam hits on the pole, because the pole is a cylinder shape. It was difficult to find the exact reference spot on the pole. In addition, the reference point on the laser scanner, a mirror, which can detect a laser beam reflected from the pole, was inside a sealed case. It also was hard to know the exact location of the mirror. Measurement error from the measuring tape was caused by inaccurate reference points on the pole and laser scanner. Therefore, averaged distance measured using the laser scanner was considered as a true distance between the pole indicator and the laser scanner. Table 1 shows results of the stationary test. Angles at which the laser scanner actually detected the pole indicator were slightly deviated from the intended angles. The standard deviations of the direct distance readings were less than 0.7 cm. The distance measurement errors were between ±0.31 and ±0.37% in the distance range of 523.2 to 684.8 cm. It was found that the measurement errors in general were not affected by measurement angles.
positions were erratic. Therefore, the first 13% and the last 5% of the data recorded were removed for statistical analysis and for figures 8 and 9. The control error oscillated with elapsed travel time. Maximum lead error, indicated by the greatest positive value, was 22.34 cm, while maximum lag error, indicated by the most negative value, was 22.11 cm. Root‐mean‐square error (RMSE) was 8.23 cm. The control error in a dynamic test with a trapezoidal travel speed change pattern is shown in figure 9. The travel speed of the master increased gradually from 0.64 to 1.14 m s‐1 during a travel distance of about 17 m, was maintained at that higher speed for about 8 m, and then decreased gradually to 0.66 m s‐1 during a distance of 19 m. It is thought that the ripple in the master travel speed might be caused by actual fluctuation of the travel speed, which was adjusted manually by an operator. Table 2 reports summarized results of the dynamic tests. At the four constant travel speeds, the maximum lead and lag errors were less than 32 and 23 cm, respectively, and the RMSE was smaller than 10 cm. The control errors measured at different travel speeds did not exhibit any relationship with the speeds. This indicated that the performance of the control system developed in this study was independent of the travel speed of the vehicles. At the trapezoidal speed pattern, the maximum lead error, maximum lag error, and RMSE were 17.30, 10.92, and 8.93 cm, respectively. These errors were similar to those obtained at the four constant travel speeds.
Table 1. Performance of the laser scanner in the stationary test. Averaged Direct Measurement Distance (R) Angle (θ) (cm) (°) 50.75 90.25 130.50
832
668.3 523.2 684.8
Standard Deviation of the Direct Distance (cm)
Difference between Maximum and Minimum Distances (cm)
Distance Measurement Error (%)
0.68 0.60 0.67
4.30 3.90 4.20
± 0.32 ± 0.37 ± 0.31
60 40 Control error (cm)
DYNAMIC TEST Figure 8 shows the control error indicated by the leading distance between the master and slave at a constant travel speed of 1.04 m s‐1 in a dynamic test. Due to difficulty in getting the test vehicles started and stopped at the same time, the control errors measured at starting and ending
20 0 -20 -40 -60 0
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60
Figure 8. Control error at a travel speed of 1.04 m s‐1 in a dynamic test.
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1.4
8
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40
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Rod retraction
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3 2 1 0
-40 0
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Figure 9. Control error with a trapezoidal travel speed pattern.
This showed the performance of the control system was not affected by gradual transition, taking about 20 s, in the travel speed of the vehicles. The maximum lead errors were generally greater than the maximum lag errors. To further investigate the sources of the control error, specifications of the actuator used in this study were examined. The stroke length of the actuator connected with the HST foot pedal was measured during extension when the input voltage for the actuator increased from 2 to 4.4 V with a 0.2 V interval, and then the voltage decreased back to 2 V to retract the rod with the same voltage interval. The test results indicated the hysteresis of the actuator (fig. 10). The average difference between the stroke lengths measured at the same voltage when the rod was on extension and retraction was 0.42 cm. This corresponded to the stroke length error of 9.3% because the full stroke length in this study was 4.5 cm. Since the stroke length is directly related to the travel speed of the vehicle, stroke length error caused by different moving directions of the actuator rod could be one of the control error sources. This also might cause the maximum lead error to be greater than the maximum lag error. The lead error occurred when the master vehicle was ahead of the slave. To increase the travel speed of the slave to catch up with the master, the input voltage actuator should decrease, and the actuator rod be retracted. Because the stroke length of the actuator on retraction is greater than that on extension at the same input voltage, the supplied input voltage for the actuator on retraction may not be enough to take the actuator rod back to the required position that is capable of increasing the travel speed of the slave to catch up with the master. This might contribute to increasing the lead error. The minimum input voltage increment or decrement level required to change the moving direction of the actuator rod was investigated experimentally and found to be 120‐mV Table 2. Performance of the control system in the dynamic test. Travel Speed (m s‐1)
Max. Lead Error (cm)
Max. Lag Error (cm)
RMSE (cm)
0.66 0.87 1.04 1.30 Trapezoidal speed pattern
24.28 30.24 22.34 31.54 17.30
13.08 17.32 22.11 20.63 10.92
6.44 8.64 8.23 9.04 8.93
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1
1.5
2
2.5 3 3.5 Input voltage (V)
4
4.5
5
Figure 10. Stroke length of the actuator on extraction and retraction based on input voltages.
DC. Although the PID controller calculated the magnitude of the input voltage with a good resolution based on the measured leading distance, and the data acquisition device generated it, the actuator could not respond to low input voltage change, thereby enhancing errors. FUTURE STUDIES The DC brush motor linear actuator used in this study showed the hysteresis, which was one of the control error sources. To improve the performance of the control system developed through this work, a different type of actuator, which can minimize the hysteresis problem, will be considered. There may be a situation in a citrus orchard that has not been tested in this study and causes error. For example, the laser beam can be blocked by unexpected objects such as poles, field structures, or other unexpected materials before it reaches the pole indicator. These unfavorable conditions in a field may increase control error and necessitate the need for a backup safety system if the system is installed on a real machine or becomes commercially available. This article only reported studies on the travel speed control of a pair of test vehicles driving in a parallel path. We are currently upgrading the control system to synchronize both forward movement and steering of the paired vehicles, expecting this additional steering control would strengthen the capability of the synchronization control system.
SUMMARY AND CONCLUSIONS In this study, a laser scanner‐based control system for synchronizing the forward movement of two test vehicles (master and slave) driving in a parallel path was developed. The control system, which consisted of a laser scanner, an electromechanical linear actuator, a data acquisition device, a LabVIEW control program, and a PID controller incorporated in the LabVIEW program, was mounted on the slave vehicle. To measure a position of the master vehicle with respect to the slave, a cylindrical‐shaped PVC pipe was mounted vertically on the master vehicle as a target object for the laser scanner on the slave vehicle. Experiments for testing the measurement accuracy and repeatability of the laser scanner under stationary conditions and the performance of the control system under dynamic conditions were conducted. For the stationary test, the master vehicle was
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located at three angles of about 50°, 90°, and 130° with respect to the slave. The intended offset distance between the master and slave was 5 m. The laser scanner on the slave measured a direct distance to the master for 1,000 readings. For the dynamic test, the master traveled at four constant speeds of 0.66, 0.87, 1.04, and 1.30 m s‐1, and a trapezoidal speed pattern with a minimum speed of 0.64 m s‐1 and a maximum speed of 1.14 m s‐1. The travel speed of the slave was adjusted by the laser scanner‐based control system to keep detecting the pole indicator on the master at an angle of 90°. The following conclusions can be drawn from these tests: S In the stationary test, distance measurement errors were between ±0.31% and ±0.37% in the distance range of 5.2 to 6.8 m. Standard deviations of the direct distances measured were less than 7 mm. It was found that the measurement error in general was not affected by measurement angle. S At the four constant travel speeds in the dynamic test, maximum lead error, which occurred when the master was ahead of the slave, and maximum lag error, which occurred when the slave was ahead of the master, were 32 and 23 cm, respectively. The lead errors in general were greater than the lag errors. Root‐mean‐square error (RMSE) was smaller than 10 cm. The performance of the control system was independent of the travel speed of the test vehicles. S At the trapezoidal speed change pattern, the maximum lead error, maximum lag error, and RMSE were 17.30, 10.92, and 8.93 cm, respectively. These errors were similar to those obtained at the four constant travel speeds. This showed the performance of the control system was not affected by smooth speed transition which took about 20 s. S Test results indicated that the laser scanner‐based control system developed in this study successfully synchronized the forward movement of two test vehicles driving in a parallel path. However, the error sources caused by the actuator used in the tests will need to be addressed to decrease the control errors.
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ACKNOWLEDGEMENTS This research was supported by the Florida Agricultural Experiment Station and a grant from the Florida Citrus Initiative program. The mention of product and company names is for information only and does not imply an endorsement or recommendation by the University of Florida.
REFERENCES Kise, M., Q. Zhang, and N. Noguchi. 2005. An obstacle identification algorithm for a laser range finder‐based obstacle detector. Transactions of the ASAE 48(3): 1269‐1278. LabVIEW. 2001. PID Control Toolset User Manual. Austin, Tex.: National Instruments Corp. Martínez, J. L., A. Pozo‐Ruz, S. Pedraza, and R. Fernández. 1998. Object following and obstacle avoidance using a laser scanner in the outdoor mobile robot Auriga‐a. In Proc. 1998 IEEE/RSJ Int. Conf. on Intelligent Robots and Syst., 204‐209. Piscataway, N.J.: IEEE. Ogata, K. 1997. Modern Control Engineering, 3rd ed. Upper Saddle River, N.J.: Prentice Hall. Reina, A., and J. Gonzalez. 1997. Characterization of a radial laser scanner for mobile robot navigation. In Proc. 1997 IEEE/RSJ Int. Conf. on Intelligent Robots and Syst., 579‐585. Piscataway, N.J.: IEEE. Subramanian, V., and T. F. Burks. 2005. Autonomous path navigation in citrus groves using machine vision and laser radar. ASAE Paper No. 051142. St. Joseph, Mich.: ASAE. Tsubota, R., N. Noguchi, and A. Mizushima. 2004. Automatic guidance with a laser scanner for a robot tractor in an orchard. In Proc. 2004 Conf. Automation Tech. for Off‐Road Equipment, 369‐373. St. Joseph, Mich.: ASAE. White, R., and M. Tomizuka. 2001. Autonomous following lateral control of heavy vehicles using laser scanner radar. In Proc. 2001 American Control Conf., 2333‐2338. Piscataway, N.J.: IEEE. Ye, C., and J. Borenstein. 2002. Characterization of a 2‐D laser scanner for mobile robot obstacle negotiation. In Proc. 2002 IEEE Int. Conf. on Robotics and Automation, 2512‐2518. Piscataway, N.J.: IEEE.
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