*Optimized Coverage Path Planning and Headland Turning Trajectory Optimization for Auto-Steer Agricultural Field Equipment

Transcription

1 *Optimized Coverage Path Planning and Headland Turning Trajectory Optimization for Auto-Steer Agricultural Field Equipment Lie Tang, PhD Associate Professor Agricultural Automation and Robotics Laboratory Department of Agricultural and Biosystems Engineering Iowa State University Tel: *This presentation is based on the dissertation research of my former PhD students: Dr. Jian Jin & Dr. Xuyong Tu.

2 Optimized Coverage Path Planning Why Coverage Planning Currently farmers plan the operation path based on experiences Auto-guidance system can only follow existing parallel paths The good path should Travels over field surfaces Minimizes time and other costs Be coordinated with specific field operations and topographical land features USDA

3 Optimization Process 2D Planning 3D Planning

4 Basic Strategy & Algorithm Divide and Conquer What is the best way of decomposing the field into subregions when necessary? What is the optimal coverage direction for covering each region? A Recursive Algorithm Fabret et al. (2001)

5 Headland Turning Cost with boustrophedon paths

6 Cost Function The number of turns on the i th edge is L i cos( ) / 2w i p C Ci The total cost: where p is the number of edges and i 1 Ci is the cost on the i th edge. We need to minimize the total cost by choosing a value for [0,180 )

7 Turning Cost of Different Patterns flat turn: U-turn: bulb turn: asymmetric bulb turn or hook turn:

8 Decision Tree on Turning Pattern Selection Determine the turning pattern: Vehicle s minimum turning radius Swath width Headland width

9 Divide into 2 Sub-regions Step 1: Construct the network-like gragh From each vertex (including the vertices on the internal holes), draw the rays into the internal area of the field. Step 2: Depth-first search in the graph Starting from a vertex on the outside boundary, ending at another vertex on the outside boundary; An example dividing route:

10 Running Time For a field with m obstacles and totally n edges : m 1 m 1 T( m, n) O( n log( n ))

11 Field Representation Planar geometry models Polygons, Planar Subdivisions, and so on A planar subdivision represented by a DCEL (Doubly Connected Edge List); Field Boundary Simplification

12 Field Boundary Simplification Advantages of the new boundary simplification algorithm over Douglas Peucker: Minimizes both distance and direction error; Eliminates integrated error; Reserves critical points; Douglas Peucker s result Wavelets-based algorithm s result

13 Results of 2D planning for planar fields Try square shape: Decompose it into two rectangular shapes. The covering direction is along the longer edges.

14 Results of 2D planning for planar fields The left figure is the result given by Fabret et al. (2001). The right figure is the result generated by our algorithm.

15 Results of 2D planning for planar fields Add some obstacles within the field.

16 Results of 2D planning for planar fields An example of a complex field.

17 2D Result Farmer s approach OPP output Saving of OPP on the number of turns: 9% Saving of OPP on the headland turning cost : 4%

18 Paths on 3D - Soil Erosion Cost The Revised Universal Soil Loss Equation (RUSLE) : A=R*K*L*S*C*P The relative effectiveness of contouring for controlling erosion on various slopes is shown by the conservation practice factor P (Schwab et al., 1993) P is the support practice factor (USDA Agriculture Handbook,1997) The incurred soil erosion is estimated by averaging throughout the whole terrain surface:

19 Paths on 3D - Curved Path Cost There could be various types of costs from the curved paths : Operator Fatigue Uneven Rates Inconsistent Spacing between Swaths Lower Speed Influence to the GPS Auto-Guidance System Influence on the Implement In this project, the sum of skipped areas resulted from the paths high curvatures was calculated as an indicator of the cost from the curved paths

20 Integration of Different Cost All the three costs were considered for the whole 3D planning cost function These costs were measured in different ways the headland turning cost was in form of the time spent during the turnings the soil erosion cost was in form of the support practice factor, P in the RUSLE equation the curving cost was in form of the summed skipped area from the sharp turnings The calculated cost values of each category were normalized before they were summed The total cost function is in the form of

21 Path Planning Example Field Information 3D Surface Plot Location Area Southwest Iowa 120 acres Maximum Slope 16.5% Average Slope 3.1% Satellite Image Contour View

22 Path Planning Example Decomposition 2D Planning Result

23 Path Planning Example Recommended Comparison of Different Cost Min Erosion Edge 1 Comparison of Summed Cost (Weights 1:1:0.5) Edge 2 Edge 3

24 Path Planning Example Cost Comparison between 2D and 3D Results in Region 4 Combined Result Cost Type Saving of 3D Planning Turning Cost -36.0% Erosion Cost 69.5% Skipped Area Cost 100% Summed Cost 36.1% Farmer s Approach Improved Result

25 Related Publications Jin, J. and L. Tang Optimal coverage path planning for arable farming on 2D surfaces. Transactions of the ASABE 53(1): Jin, J., L. Tang Coverage path planning on threedimensional terrain for arable farming. Journal of Field Robotics 28(3):

26 Headland Turning Optimization

27 Headland Turning Framework

28 Headland Turning Framework Formulation Initial condition: Final condition: Boundary conditions and constraints:

29 Objective Function Minimizing the time of turning t J min X = f 1 t o dt

30 Tractor-only Model

31 Tractor-Trailer Model

32 Tractor-Trailer-Trailer Model

33 An Example: Tractor Symmetric Bulb Turn with constant velocity DCNLP result (sec) Analytical result (sec) Error (sec) Error percentage %

34 Headland Turning Trajectory Optimization: with revised Headland Angle Prohibited area Headland

35 With steering and acceleration controllable Prohibited area Headland

36 Fish Tail Turn Within Tighter Headland Prohibited area Headland

37 Headland Turning Optimization: with One Single-axle Implement

38 Headland Turning Optimization: with Two Single-axle Implements

39 Conclusions A research framework of agricultural vehicle headland turning optimization has been mathematically formulated. Direct numerical method was used to generate optimal turning trajectory. The kinematic models of different vehicle structures were investigated in this framework. Diverse headland turning scenarios were proposed and studied.