Corrigendum to Determination of an Optimal Return-Path on Road Attributes for Mobile Robot Recharging
Authors: Liu Fei , Liang Shan , Xian Xiaodong 
Published: November 2012

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, ceincludes two parts, the part that the sensors on the robot will consume, and secondly, the energy used for driving the motor. Here, we use csto describe the first part and use ĉeto describe the second part. Therefore, [Formula: see text] Then the cost Ccan be described as[Formula: see text] 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 [Formula: see text] (4) In column 2, Equation (11) should be [Formula: see text] Page 87 (1) In column 2, Equation (20) should be [Formula: see text] 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 rsas the energy consumption rate, which describes how much energy the sensor will consume when the robot walks for a unit distance. The value of rsis always stable, so for any road segment, for passing distance pml, we have the energy consumption[Formula: see text] (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: [Formula: see text] Here, we do not measure rsdirectly, 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[Formula: see text] We assume that the robot walking for distance pml at average speed v̄ (unit: m/s), then [Formula: see text] In our experiment, we set Vstart = 12.7 V, Vend = 11.3 V, v̄ = 0.75 m/ s, then it is measured that t = 4.5 h, therefore, rs is measure to be [Formula: see text] (2) Equation (38) should be [Formula: see text] (3) Equation (39) should be [Formula: see text] (4) Equation (40) should be [Formula: see text] (5) Equation (41) should be [Formula: see text] (6) Equation (42) should be [Formula: see text] Page 90 (1) Equation (45) should be [Formula: see text] (2) In the penultimate paragraph of column 2, the following corrections should be made: As listed in Table 2 , the cost CRD0 n is (0.0520,0.8693×10−3) and the idle time TIDLE_ RD0 is 346.834 s. [Table: see text] (3) Equation (50) should be [Formula: see text] 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 δ TIDLE = 20.694 s is taken as an example, ( 3 ) Equation (51) should be [Formula: see text] (4) Equation (52) should be [Formula: see text]