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16 CHAPTER 3. FUNDAMENTALS B T 1 T 2 T 3 T 4 A dT req dT res Figure 3.6: Way to get the current time from a time server. Figure 3.6 shows an example, where A wants to synchronize to B. To do this, A sends a request to B, stamped with the time value T 1 . If the message is received, B will record this time T 2 . B then sends a response to A containing T 2 and T 3 . Finally A records the time T 4 when the message from B was received. It is assumed that the message delay from A to B is roughly the same than from B to A. This means that T 2 − T 1 ≈ T 4 − T 3 . Thus, in this example A can estimate delay δ and its offset θ to B as 3.3.2 PTP (Precision Time Protocol) δ = (T 2 − T 1 ) + (T 4 − T 3 ) and (3.2) 2 θ = T 3 + δ − T 4 . (3.3) To get better clock synchronization than achievable by NTP the Precision Time Protocol (PTP) was designed [13]. It is for example used in industry for industrial automation or robotic control. With special network cards and switches a synchronization accuracy of 10-100 nanoseconds is achievable. With normal network components and a software implementation of PTP a synchronization accuracy of 10-100 microseconds is possible [22]. The Precise Time Protocol synchronizes clocks between a Master and a Slave, similar to the Network Time Protocol. The Master provides the time and one or more Slaves synchronize to the Master. Therefore the Master sends Sync messages, typically every two seconds to the Slaves. Further the Slaves send less frequently, about one request per minute, Delay Request messages to the Master to determine the network delay, which is needed for time correction. The four timestamps needed for accurate time synchronization are T 1 , T 2 , T 3 and T 4 (see Figure 3.7) [22]. When the Master is sending the Sync message, T 1 is captured. T 1 is then later send to the Slave via the Sync Follow up message. The Slave captures T 2 when the Sync message is received and T 3 when it sends the Delay request message. When the Master receives the Delay request message, it records T 4 and sends it back to the Slave with the Delay Response message. The Slave can now calculate the delay δ with Equation 3.2 and the offset θ with θ = T 2 − δ − T 1 . The Precision Time Protocol allows sufficient time synchronization for applications on mobile robots where the normal frequency of data capturing is not higher than 50 Hz which is 20 ms. Thus the uncertainty introduced by the measurement error is far higher than the one introduced by the inaccuracy of the time synchronization. Further it is easy to setup PTP on the Linux operating system,
3.3. TIME SYNCHRONIZATION 17 Master Clock Slave Clock T 1 Sync message T 2 Sync Follow up message Delay Request message T 3 T 4 Delay Response message Time Figure 3.7: Clock synchronization in PTP. which is widely used in robotics. For Linux a daemon called PTPd exists, which works with normal network hardware. It is shown in [7] that a synchronization accuracy of 10-100 µs can be reached with PTPd.
Page 1: Managing Coordinate Frame Transform
Page 5: Abstract Autonomous mobile robots i
Page 9 and 10: Contents 1 Introduction 1 1.1 Intro
Page 11 and 12: Chapter 1 Introduction 1.1 Introduc
Page 13 and 14: 1.2. OVERVIEW OF THE TRANSFORMATION
Page 15 and 16: Chapter 2 Related Work This chapter
Page 17 and 18: 2.2. COMPONENT-BASED ROBOTIC MIDDLE
Page 19 and 20: Chapter 3 Fundamentals In this chap
Page 21 and 22: 3.2. TRANSFORMATIONS 11 This transl
Page 23 and 24: 3.2. TRANSFORMATIONS 13 the popular
Page 25: 3.3. TIME SYNCHRONIZATION 15 3.3 Ti
Page 29 and 30: Chapter 4 Method At the beginning o
Page 31 and 32: 4.1. USE CASES 21 (a) Tilting plana
Page 33 and 34: 4.2. ANALYSIS OF REQUIREMENTS 23 To
Page 35 and 36: 4.3. ABSTRACT SYSTEM DESCRIPTION 25
Page 37 and 38: 4.3. ABSTRACT SYSTEM DESCRIPTION 27
Page 39 and 40: 4.4. QUALITY OF TRANSFORMATIONS 29
Page 45 and 46: 4.5. CLIENT/SERVER SEPARATION 35 va
Page 47 and 48: 4.5. CLIENT/SERVER SEPARATION 37 Da
Page 49 and 50: 4.6. CONSTRUCTING TF SYSTEMS 39 val
Page 51 and 52: 4.6. CONSTRUCTING TF SYSTEMS 41 bas
Page 53 and 54: 4.6. CONSTRUCTING TF SYSTEMS 43 1.8
Page 55 and 56: 4.6. CONSTRUCTING TF SYSTEMS 45 •
Page 57 and 58: tilt_frame sensor_frame 4.6. CONSTR
Page 59 and 60: Chapter 5 Results To better examine
Page 61 and 62: 5.1. SIMULATION 51 • the torso_fr
Page 63 and 64: 5.2. DISCUSSION OF THE RESULTS 53 l
Page 65 and 66: Chapter 6 Summary and Future Work 6
Page 67 and 68: List of Figures 1.1 Three state-of-
Page 69 and 70: List of Tables 3.1 Comparison of ma
Page 71 and 72: Bibliography [1] N. Ando et al. “

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