Fei Liu, Shan Liang, Xiaodong Xian

Nov 1, 2012

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Influential Citations

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Citations

Journal

International Journal of Advanced Robotic Systems

Abstract

This corrigendum is offered as a means to correct errors in “Determination of an Optimal Return-path on Road Attributes for Mobile Robot Recharging” (Fei Liu, Shan Liang, Xiaodong Xian, International Journal of Advanced Robotic Systems, vol.8, no.5, pp. 83–92, 2011). The error is due to the fact that we reckoned without taking into account the energy consumed by the sensors on the robot. Please see the corrections below. Page 85–86 (1) In column 2, the last paragraph should read: (c) The cost that the robot will pay for passing each segment includes two parts: energy consumption ce and the influence of vibration on the robot body cb that describes the probability of the robot's equipment failure. Actually, ce includes two parts, the part that the sensors on the robot will consume, and secondly, the energy used for driving the motor. Here, we use cs to describe the first part and use ĉe to describe the second part. Therefore, (1) c e = c ^ e + c s Then the cost C can be described as (2) C = ( c e , c b ) Page 86 (1) In column 2, the chapter title “4.2.1 Mathematical Model of ce “ should read: “4.2.1 Mathematical Model of ĉe”. (2) In column 2, the paragraphs after Equation (9) and before Equation (11), all ce should be replaced by ĉe. (3) In column 2, Equation (10) should be (3) c ^ e = λ W P m l (4) In column 2, Equation (11) should be (4) c ^ e = r e p m l Page 87 (1) In column 2, Equation (20) should be (5) c ^ e =( Δ r e _ r p m r cos ( p m g ) + Δ r e _ g sin ( p m g ) ) p m l Page 88 (1) In column 1, after Equation (25) in chapter 4.2.2, the following should be added: 4.2.3 Mathematical Model of cs First, we define rs as the energy consumption rate, which describes how much energy the sensor will consume when the robot walks for a unit distance. The value of rs is always stable, so for any road segment, for passing distance pml , we have the energy consumption (6) c s = r s p m l (2) In column 2, chapter title “4.2.3 Computing the Idle Time” should be replaced by “4.2.4 Computing the Idle Time”. Page 89 (1) In column 1, after the first paragraph in chapter 5.1, the following should be added: ( a ) r s Here, we do not measure rs directly, on the contrary, we first measure the consumption rate for unit time, which can be termed τ s (unit: V/ s). If Vstart (unit: V ) is the voltage value when the robot is just powered on, and after a period of time t , the value decreases to V end (unit: V), we get (7) τ s = V s t a r t − V e n d t We assume that the robot walking for distance pml at average speed v̄ (unit: m/s), then (8) r s = τ s v ̄ In our experiment, we set Vstart = 12.7V, Vend = 11.3V, v̄ = 0.75m/s, then it is measured that t = 4.5h, therefore, rs is measure to be (9) r s = 12.7 V − 11.3 V 0.75 m / s × 4.5 h × 3600 s / h ≈ 0.1152 V / m (2) Equation (38) should be (10) r e = V s t a r t − V e n d v ̄ t ̄ − r s (3) Equation (39) should be (11) r e _ μ f = 12.7 V − 11.3 V 0.75 m / s × 2.67 h × 3600 s / h − 0.1152 × 10 − 3 V / m ≈ 0.0790 × 10 − 3 V / m (4) Equation (40) should be (12) r e _ μ r = 12.7 V − 11.3 V 0.75 m / s × 2.07 h × 3600 s / h − 0.1152 × 10 − 3 V / m ≈ 0.1353 × 10 − 3 V / m (5) Equation (41) should be (13) μ r = r e _ μ r r e _ μ f μ f = 0.1353 × 10 − 3 0.0790 × 10 − 3 μ f ≈ 1.7127 μ f (6) Equation (42) should be (14) r e _ μ f φ g ≈ 0.2034 × 10 − 3 V / m − 0.1152 × 10 − 3 V / m = 0.0882 × 10 − 3 V / m Page 90 (1) Equation (45) should be (15) η = r b _ μ r μ f r b _ μ f μ r = 0.5698 × 10 − 5 0.2645 × 10 − 5 × 1.7127 ≈ 1.2578 (2) In the penultimate paragraph of column 2, the following corrections should be made: As listed in Table 2, the cost CRD0n is (0.0520,0.8693×10−3) and the idle time TIDLE_ RD0 is 346.834s. Table 2. The optimal return-path to each dock Dh(h = 0, 1, 2) as well as the constitution of each RDh (h = 0, 1, 2), the total path length LT, the cost and the idle time. Dh D 0 D 1 D 02 RD h {PSRO, P21,P0} {PSRP, P19,P9} {PSRP, P16,P17} LT/m 262.1 282.9 246.4 ( C e , C b ) (0.0520, 0.8693 ×10−3) (0.0544, 2.4780 × 10−3) (0.0529, 1.1827 × 10−3) TIDLE /S 351.361 390.160 372.055 (3) Equation (50) should be (16) Δ T I D L E = 366.547 s − 346.834 s = 19.713 s Page 91 (1) Table 2 should be replaced by (2) In column 2, in the paragraph below Table 2, the following corrections should be made: Statistically, if the robot returns to recharge four times a day on average and δTIDLE = 20.694s is taken as an example, (3) Equation (51) should be (17) T S A V E = 19.71 s × 4 × 360 3600 s / h = 7.88 h (4) Equation (52) should be (18) N = T S A V E T M T T R = 7.88 h 4 h = 1.97

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