Hokuyo URG-04LX-UG01 Laser Range Finder Tree Diameter Measurement Algorithm

2.1. Hokuyo URG-04LX-UG01 Laser Range Finder

Hokuyo LRF is a laser sensor with infrared light source as shown in Fig. 1. Its scanning area is about 240° at accuracy until 4000 mm as clearly illustrated in Fig. 2 [3]. Object’s color has minimum effect upon the Laser Range Finder. The specifications of URG-04LX-UG01 are summarized in Table 1. Fig. 1 Hokuyo URG-04LX Laser Range Finder Fig. 2 Detection Angle and Maximum Distance of Hokoyo LRF Table 1: URG-04LX-UG01 Power Source 5V DC from USB Detection Distance 0.02 – 4.00m Accuracy Distance : 0.02mm – 1.00m ±0.03m Distance : 0.02m – 4.00m ±3 of measurement Total Scan Angle 240 ° Weight Approximately 160g Life Span Approximately 5 years Light Source Laser Class 1 Hokuyo URG-04LX Laser Range Finder is appropriate to be used for detecting surface properties and measure conditions although it is small in size [4]. Its accuracy depends on material properties and can be calculated from the absolute error produced during measurement. Fig. 3 shows material properties used for testing URG-04LX LRF. The actual distance of the object is at 1500 mm. Aluminum is most likely to be the surface of detection because its data approaches 1500 mm. Wood material is considered very good to be the surface used for LRF detection since its data is closer to 1500 mm compare to gray sheet, steel and electrical steel. Fig. 3 Material Properties

2.2. Tree Diameter Measurement Algorithm

The basic principle behind the tree diameter measurement algorithm is based on the circle tangent theory. Cross section of tree is considered as circle and can be calculated using circle equations. From circle tangent theory if a line is tangent to a circle, the straight line drawn from circle’s radius to the point of contact between circle’s radius and the tangent line is perpendicular with both the tangent line and circle’s radius as illustrated in Fig. 4. Fig. 4 Line Tangent to Circle Now consider in Fig. 5 that consist of two lines tangent to the circle located at different contact points but both of them are extended to a same point. A straight line is drawn from the contact point up to the circle’s radius for both the tangent lines. The intersection point of both lines drawn from the two tangent lines will meet at centre point of the circle. Fig. 5 Two Lines Tangent to Circle Angle measured between the two tangent lines is represented by theta. Length a and b are both measured from extended point of both tangent lines to the contact point of the tangent lines respectively. Fig. 6 Finding the Length c From Fig. 6, length c can be calculated using law of cosines formula provided that length a, length b and θ are known: c 2 = a 2 + b 2 − 2 abcosθ 1 c= √ a 2 + b 2 − 2 abcos θ 2 Meanwhile radius of the circle, R can be calculated if length c is found and thus yield to the determination the circle’s diameter, D: θ 2 = 180 °−θ II c 2 = R 2 + R 2 − 2× R × R × cos θ 2 4 c 2 = 2 R 2 − 2 R 2 cos θ 2 c 2 = 2 R 2 [ 1−cos θ 2 ] 2 R 2 [ 1−cos θ 2 ] = c 2 R 2 = c 2 2 [ 1−cos θ 2 ] R= √ c 2 2 [ 1−cos θ 2 ] 3 Diameter of the circle, D is: D ¿ 2 R 4 Therefore, the tree diameter can be measured using the algorithm derived where the distance to measure the diameter of the tree can be varied for different set of measurements.

3. Experimental Setup