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ASAE Conference Proceeding

This is not a peer-reviewed article.

Autonomous Traveling of Off-road Vehicles along Rectangular Path on Slope Terrain

M.A. Ashraf, R. Torisu, and J. Takeda

Pp. 412-421 in Automation Technology for Off-Road Equipment (ATOE) Proceedings of the 26-27 July 2002 Conference (Chicago, Illinois, USA), ed. Qin Zhang ,Pub. date 6 July 2002 . ASAE Pub #701P0509

ABSTRACT

An automatic off-road wheeled-vehicle guidance system has been developed to navigate the vehicle along rectangular path on sloped terrain. For this purpose a neural network (NN) vehicle model was proposed to obtain relationship between the steerage and behavior of tractors on sloped terrain. An optimal control theory is applied to design a steering controller for the rectilinear motions on sloped terrain, where genetic algorithm was used to optimize the steering angle. A coordinate transformation system was also designed to determine the vehicle position with respect to the rectangular path. Feedback control method was applied for the rectilinear motions along the contour lines, uphill and downhill directions; and feedforward control method was applied for the quarter turns of the rectangular path. Finally the feedback and feedforward control methods were compounded to guide the tractor along the rectangular path. An autonomous traveling test was conducted along a 30x15 m rectangular path on in excess of 15Ί sloped terrain. Results showed that average of the mean and standard deviations of lateral displacements and heading angles for the motions along four directions of the rectangular path were 0.05 m, 0.06 m, -0.1Ί and 2.3Ί respectively.

KEYWORDS. Autonomous travel, Off-road vehicle, Rectangular path, Slope terrain, Optimal control, Neural Network, and Genetic Algorithm

Introduction

Considerable grasslands or meadows of Japan are in hilly areas where farm machines perform various task. When a human operator conducts any farming operation with vehicle on sloping ground, he feels discomfort due to a faulty body posture. Continuous body posture adjustment results in operator fatigue. This causes decrease in work-efficiency and increases the operator mental stress. Therefore, to give a relief to the human operator from such tedious work, other alternatives such as autonomous vehicles for slope-land farming for the 21st century should be considered.

Many researches on tractor guidance system have been done in advanced countries (Torii, T., 2000; Keicher et al., 2000; Reid et al., 2000; Mizushima et al., 2000), but most of those are for flatland environment. Bell (2000) conducted research on the vehicle guidance on sloped terrain where he used kinematic vehicle model. But the kinematic model cannot incorporate the downward slip of vehicle. To compensate for this limitation he added biased estimation (Bell, T., 1999) method in his model. This study proposes another approach on automatic tractor guidance system that would run autonomously along the rectangular path on sloped terrain. To reduce the soil erosion on sloped terrain, contour farming is a well-known practice, where tractors travel along rectangular paths. Therefore, the objective of this paper is to design and develop an autonomous tractor that can precisely travel along the rectangular path on sloped terrain. This paper discusses the following: 1) formulation of vehicle model on sloped terrain by neural network (NN); 2) a navigation planner for the rectangular path; 3) the closed-loop steering controller for the rectilinear motions using optimal control method, and its optimization, using “genetic algorithm (GA)”; 4) an open-loop steering controller for the quarter-turn of a tractor, 5) combination of the closed-loop and open-loop control methods for rectangular path control; and 6) installation of necessary sensors and trial production of the steering mechanism.

Formulation of vehicle model for sloped terrain

Structure of vehicle model

412-421_files/image1.gif

412-421_files/image2.gif 412-421_files/image3.gif

Figure 1 shows a bicycle model of a tractor with slope influence. Whenever an agricultural wheeled vehicle moves on sloping land, external disturbances such as gravitation force pull it to the downhill direction, which causes strongly nonlinearity in the vehicle dynamics. Consequently, it is quite difficult to formulate either a kinematic or dynamic model to express the vehicle motion on sloped terrain. Recently there has been an increase in the number of applications of NN in various engineering and biological problems (Morishita et al., 1993). Therefore, a NN vehicle model is considered to express the input-output relationship of vehicle motion on sloping land. The adjusted interconnecting weights of the neurons in NN can include all of the effective elements such as slippage due to gravity, uneven condition of the slope and other external influences. Till to date, as could be ascertained only Noguchi et al. (Noguchi et al., 1997, 1993) used NN for agricultural vehicle modeling. The architecture of the neurons (later denoted as units) of his model was 5-5-5-3, which had 5 input and 3 output variables together with two hidden layers of 5 units each. His model was successful on flat land. Prior to the development of our NN based vehicle model, we used Noguchi’s model. However, it was not possible to train up his model for sloped terrain conditions. Therefore, we expanded and modified Noguchi’s model to make it applicable for sloped terrain. The architecture of the developed NN vehicle model was 6-6-6-3.

Since the vehicle motion on slope is strongly nonlinear, a multi-layer network was considered that consists of input, output and two hidden layers. The output layer had 3 units and the others had 6 units each. The architecture of the developed NN vehicle model is shown in Fig. 2. The input vector is a combination of the control vector U k , and state vector Z k , and the output vector is ? k+1 , which is also known as target vector.

where,

412-421_files/image4.gif ……………(1)

412-421_files/image5.gif …….(2)

412-421_files/image6.gif …….. (3)

The control vector U k is a function of steering angle a and rate of steering 412-421_files/image7.gif (refer to Eq. (5)). The coordinate O-XY is the earth fixed coordinate system and G-xy is the vehicle fixed coordinate system in Fig. 1. The elements of vector Z k are Vx , Vy , 412-421_files/image8.gif and 412-421_files/image9.gif . Vx is a component of the velocity V along the longitudinal axis of the tractor body and Vy is the component perpendicular to the longitudinal axis. 412-421_files/image10.gif is the attitude angle and 412-421_files/image11.gif is the yaw rate which is defined in Eq. (10). The subscript k means equally spaced time step ( k =1,2,3…n) in a discrete system. The output vector represents the vehicle state after each 0.5 seconds ( ? t ). The output is determined by both the current inputs and their previous outputs. For this reason the network exhibits properties very similar to short-term memory in humans.

Data acquisition test of training pairs for the NN model

Data acquisition test of training pairs for the NN model was conducted on 0 ° , 5 ° , 11 ° and 15 ° sloped terrains. For each sloping land a skilled human operator operated the test tractor along a predetermined sinusoidal path, which was traced on the ground by means of rope and pegs. The directions of the sinusoidal paths were along the contour lines. Equation (4) was used to construct the sinusoidal path as shown in Fig. 3.

Fig. 3. Sinusoidal path on contour line to prepare training pairs

412-421_files/image12.gif

412-421_files/image13.gif …… (4)

The vehicle forward velocity was 0.5 m/s, and after every 0.5 sec sampling time, the vehicle locations were marked on the ground by spraying colored ink from a pressurized intravenous drip container mounted on the tractor. Recording of vehicle heading angle, steering angle and engine speed were also synchronized with the ink spraying. Vehicle positions were measured using a laser positioning system, i.e., Total Station with its prism. Location of vehicle center of gravity G( XG , YG ) was calculated from the position of ink-sprayed and heading angle. Using Eq. (5) to (12) and referring to Fig. 1, the other variables of training pairs were calculated from the recorded data:

412-421_files/image14.gif ……..(5) 412-421_files/image15.gif ……(6) 412-421_files/image16.gif …… (7)

412-421_files/image17.gif …… (8) 412-421_files/image18.gif …… (9) 412-421_files/image19.gif …… (10)

412-421_files/image20.gif …… (11) 412-421_files/image21.gif ……… (12) 412-421_files/image22.gif ……... … (13)

The steering angle a was within the range between -40 ° to 40 ° . However, due to the limit of the threshold function (Wasserman, P.D., 1989) of NN, any value beyond the range [0, 1] cannot be used in the NN model. Therefore, all the variable values were normalized to the range between 0 and 1 to make them usable for the network. The normalization procedure for the values of steering angle is shown in Eq. (13), where a max is the maximum limit of steering.

Training of NN model by BP algorithm

A supervised training method (Wasserman, P.D.,1989) was used to train up the NN vehicle model, which required the pairing of each input vector with a target vector representing the desired output. These two vectors together are called a training pair (Wasserman, P.D., 1989). The NN model was trained by back propagation (BP) algorithm so that application of a set of input would produce the desired set of output. A set of 90 training pairs was used for this purpose. The training was accomplished by sequentially applying the input vector. In each step, errors were calculated from the difference of desired output and actual output, and were fed back to the network to adjust the weights according to the following Eq. (14) to Eq. (16):

412-421_files/image23.gif .. (14) 412-421_files/image24.gif ..(15) 412-421_files/image25.gif …(16)

The training process continued until the error for the entire training set was at an acceptably low level. The steepest decent algorithm was used in this study to minimize the errors. This training is a trial and error method. There is no assurance that the model will be properly trained. Therefore, after the end of each trial of training, a simulation was done with the trained model in order to check the accuracy of training achieved. Only the value of the rate of steering ? a was used as the input parameter of NN model from the actual raw data. Other variable values of the input vector were calculated after every 0.5 sec. Then the simulated sinusoidal trajectory obtained from the output of trained model was compared with the actual trajectory. The training and checking procedure continued until the difference between the actual and simulated trajectories reached to a reasonable level of accuracy.

Rectangular path planning

Structure of the rectangular path

A schematic diagram of a rectangular path on sloped terrain is shown in Fig. 4(a) and its top view in Fig. 4(b). It consists of four rectilinear paths (A1A2, B1B2, C1C2, and D1D2) and four quarter-turns (A2B1, B2C1, C2D1, and D2A1). The path A1A2 and C 1C2 were along contour lines on the sloped terrain. Path B1B2 was along the uphill direction and D1D2 was along the downhill direction. When a tractor runs from path 1 to 2, the longitudinal axis of the tractor body rotates 90 degrees from the x- axis. Therefore, to develop a navigation planner for rectangular path, it is necessary to transform the coordinate according to the change of path directions.

Fig. 4. Rectangular path on sloped terrain

412-421_files/image26.gif

Coordinate transformation

When the coordinate transformation occurs from one path to the next adjacent path, for example, from path1 to path2, two variables such as lateral displacement YG and heading angle ? should also be transformed. Figure 5 shows the rotation of the coordinate axis. An arbitrary point was chosen as the origin O and the vehicle-positioning sensor ‘Total Station’ is set at another point S . The line connecting these two points S and O was set as the X -axis and considered as a baseline. Then the heading angle of the tractor was initialized as zero along the baseline. The rotational coordinate for the adjacent path i and i+ 1 can be expressed as:

Fig. 5. Rotation of the coordinate axis

412-421_files/image27.gif

412-421_files/image28.gif … (17)

where X , Y are the earth-fixed coordinate; i is the path number ( 412-421_files/image29.gif ); and X i , Yi are the new coordinates of path i. Here the right most term of Eq. (17) is a vector and is defined as follows:

412-421_files/image30.gif .

where, L is the length and W is the width of the rectangular path.

Steering controller

Feedback control for rectilinear motion

Optimal control and state estimation

When a human operator drives a tractor along the contour line on sloped terrain, significant slippage occurs toward the downhill. In such a situation, he uses multi-feedback control techniques to control the tractor. A mathematical statement of the optimal control (Dutton et al., 1997) problem consists of: (1) the system to be controlled is described by a NN vehicle model; (2) system constraints and possible alternatives are described with steering angle a and state variables; (3) the task to be accomplished is to run along the contour line on the slope; (4) the criterion for judging the optimal performance is a quadratic form cost function J defined in Eq. (18). The control input u and state vector X are defined in Eqs. (19) and (20) respectively.

412-421_files/image31.gif ……(18) 412-421_files/image32.gif …….. (19)

412-421_files/image33.gif ……….. (20) 412-421_files/image34.gif …………… (21)

412-421_files/image35.gif ………………….. (22)

where k 1 , k3 and k4 are weights, whose values were determined by simulation.

Searching Optimum control input by GA

Genetic Algorithm (GA) (Goldberg, D.E., 1987) was applied in this study to search the optimum steering angle for each specific range of state vector. In the optimization process steering angle a depends on the lateral displacement YG , and the heading deviation ? , which can be shown by Eq. (23):

a f (k) = ƒ ( YG(k) , ? (k) ) ……………(23)

The subscript f indicates the degree of slope for which the steering will be optimized. The number of individuals or strings of the population used in this searching algorithm was 50. In optimization each set of 3 cm lateral deviation and 3° heading errors were considered as a feature (gene) of the individual, and steering angles, within the range of ± 20°, were directly coded as the feature value (allele) for each feature. Table 1 shows a sample lookup table of optimal steering angle for the range of ±9 cm lateral displacement and ±6 ? heading angle on 15 ? sloped terrain.

Total number of features was 24. Initially the feature values were randomly selected for all 24 features. Crossover and mutation rates (Goldberg, D.E., 1987) used in this study were 0.6 and 0.05 respectively.

A 20 m long contour line was considered as the target linear path to follow in the optimization process. In each step, for one set of lateral displacement and heading angle error, GA was used to find the optimum steering angle. The flowchart of steering optimization by GA is shown in Fig. 6. Equation (24) was used to determine the fitness of individuals.

412-421_files/image36.gif …………… … (24)

where, LP is a safety factor to avoid infinity when the value of J will be 0.

Table 1. A sample lookup table of optimal steering angle for 15 ° slope terrain

Lateral deviation, YG [cm]

6 ~ 9

3 ~ 6

0 ~ 3

0 ~ -3

-3 ~ -6

-6 ~ -9

Heading angle ? [ ° ]

3 ~ 6

-7

-3

1

2

3

5

0 ~ 3

-3

0

2

3

7

9

-3 ~ 0

1

3

5

7

9

13

-6 ~ -3

3

5

7

9

13

16

Fig. 6. Flowchart of steering optimization by GA

412-421_files/image37.gif

Lookup tables of optimal steering angle for 0 ° , 5 ° , 11 ° and 15 ° sloped terrains were prepared. During the travel of the tractor, appropriate optimal steering angle was selected from the corresponding lookup table with respect to the degree of slope f and deviations. A block diagram of the closed-loop control system is shown in Fig. 7.

Fig. 7. Block diagram for rectilinear motion control

412-421_files/image38.gif

The lookup table of the optimal steering angle was made only for the vehicle motion along path 1. When the vehicle travels along the contour line, uphill steering effort is larger than downhill steering effort since the gravitational force pulls the tires towards the downhill. To use the same lookup table for guiding the tractor along path 3, the sign of the two variables YG and ? were changed and then the corresponding optimal steering angle was chosen from the lookup table.

The direction of path 2 was towards the uphill and that of path 4 was towards the downhill. It was assumed that in both cases the deviations of lateral displacement and heading angle in left and right side of the path are symmetrical. Therefore, the optimal steering angles for flat land (0 ° slope) were used to guide the tractor along path 2 and 4.

Feedforward control for the turning motion

It is quite difficult to accomplish the feedback control method in the guidance of a vehicle along curved path. Therefore, feedforward control method was applied to guide the tractor along four quarter-turns of the rectangular path. Let it consider that the tractor is running along path 1 (rectilinear motion) and its turning process is shown in Fig. 8. Two parameters determine the switching from feedback to feedforward control and vice versa. The distance ? determines the initial time t 1 and

Fig. 8. Quarter turn of the rectangular path

412-421_files/image39.gif

the heading angle ? determines the final time t 2 in the feedforward control. The values of ? and ? were determined by trial and error method during supplementary field test. When the tractor reaches the predetermined point A2 (XG( t 1), YG ( t 1)) as shown in Fig. 8(a), the control method switches over from feedback to feedforward. The state vector at this initial time and final time can be expressed by Eq. (26) and (27).

412-421_files/image40.gif ………… (26) 412-421_files/image41.gif ………… (27)

The typical time histories of the steering and heading angles for the turning motion are shown in Fig. 8(b) and 8(c) respectively. As shown in Fig. 8(b), the steering angle a ( t 1) begins to increase and when it reaches the maximum ( a max), it remains constant until the heading angle of the tractor reaches a predetermined turning angle ? (Fig. 8(c)) at time t 2. Just after reaching this turning limit, the feedforward control switches over to the feedback control for the next path. Therefore, the final condition of the feedforward control in the quarter-turn becomes the initial condition of feedback control for the next rectilinear path. The open-loop control block diagram of the quarter-turn is shown in Fig. 9.

Fig. 9. Feedforward block diagram of the quarter turn

412-421_files/image42.gif

Test Field and Instrumentation of the test tractor

Test field and experimental conditions

Field test on automatic tractor guidance system was conducted on a meadow at the hilly areas of the Iwate University Omyojin Research Farm. The surface of the meadow was undulating and covered with grass. The test run was performed along a 30x15 m rectangular path. The travel direction of the rectilinear path 1 was along a contour line of 10 ° average slope and that of the path 3 was along a contour line of 18 ° average slope (Fig. 4). The tractor velocity was 0.5 m/s throughout the test.

Instrumentation

The test tractor used in this experiment was a 4WD 18 kW four-wheel drive Mitsubishi MT2501D model. Total mass of the tractor was 1125 kg, wheelbase was 1.595 m and tread was 1.31 m. High lug tire was used for the test. The tractor was equipped with a 100 MHz Pentium PC as the sensor-signal processor and steering control unit. It was also equipped with a DC motor as the steering actuator, a potentiometer to measure the steering angles and a fiber optic gyroscope (FOG) to measure the heading angles. The tested tractor and instrumentation is shown in Fig. 10. The equipment used to measure the vehicle positions was a Total Station of Leica TCA1105 model. A prism, as a pair of Total Station, was mounted on the tractor rear. Two SS wireless modems were used to transmit the signals of the tractor-position from the Total Station to the PC. To get precise-control on the vehicle, 0.5 sec was decided as the data transfer time interval.

412-421_files/image43.gif

Results and Discussion

Rectilinear motion

Figures 11 and 12 show the trajectory of the autonomous travel along the rectangular path on sloped terrain in 2-D and 3-D respectively. The point O was the starting point of the trajectory. Path 1 and 3 were assumed as the contour lines. As shown in Fig. 12 the elevation at the starting point of path 1(point O ) was 0.427 m, and at the endpoint was –0.297 m. The elevation at the starting point of path 3 was 2.67 m, and at the endpoint was 4.22 m. The average land-inclination of path 1 was 10 ° and that of path 3 was 18 ° . Figure 11 shows that even though the land- inclinations and elevations of path 1 and 3 are different, the navigation system could be successfully applied in both conditions.

Table 2 shows the mean and standard deviation of the lateral displacement and heading angle for paths 1-4. As the soil condition of path 3 was very loose in comparison to that of path 1, the tractor wheels were sliding more downward in path 3 than in path 1. Therefore, the deviation in path 3 was higher than that of path 1.

Figures 11 and 12 not available in html format, see PDF version

Table 2. Autonomous traveling performance for the rectilinear motions of rectangular path

412-421_files/image44.gif

As shown in Table 2, the mean and standard deviation of the lateral displacement for these two paths were very close to each other. But due to the effect of the gravitational force, the mean and standard deviation of the heading angle for uphill motion were more (within 1.3 ° ) than that of for downhill motion.

Table 2 also shows that the average of the mean and standard deviations of the lateral deviations for the four rectilinear motions were only 0.048 m and 0.057 m, and that of the heading angles were –0.095 ° and 2.26 ° respectively.

Turning performance

Figure 11 also shows that the convergence of three quarter turns A2B1, C2D1 and D2A1 were fairly good. But the quarter turn B2C1 did not converge immediately after the turn. This was due to the soil condition as mentioned before. Since there was no feedback control for the turning motion, the sliding error could not be compensated for and this error occurred.

Conclusion

An automatic off-road wheeled-vehicle guidance system was developed to navigate the vehicle along rectangular path on sloped terrain. A NN vehicle model was formulated to express the input-output relationship of vehicle dynamics on the sloped terrain. An optimal control law was designed and applying that control law, GA was used to find the optimal steering angle for each specific range of lateral deviation and heading errors. The navigation planner was successfully applied for guiding the tractor along opposite directions of contour lines and also along uphill and downhill directions of motion. A feedforward steering control method was developed for the tractor-motion in quarter-turn. Two control methods were compounded to navigate the tractor along the turns and rectilinear portions of the rectangular path. Despite the variations in land-inclination, the developed guidance system was successful to guide the tractor along the rectangular path on sloped terrain.

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