The Reflexxes Motion Libraries. An Introduction to Instantaneous Trajectory Generation
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1 ICRA Tutorial, May 6, 2013 The Reflexxes Motion Libraries An Introduction to Instantaneous Trajectory Generation Torsten Kroeger 1
2 Schedule 8:30-10:00 Introduction and basics 10:00-10:30 Coffee break 10:30-11:30 Reflexxes API Programming examples 11:30-11:45 Coffee break 11:45-12:30 Application examples Research and outlook 2
3 Introduction and Basics 3
4 Contents Online Trajectory Generation? Problem and Solution for One Degree of Freedom Extension to Multi-DOF Systems Results 4
5 Introduction Sensor integration on different motion control levels belongs to one of the keys for future advancements of robotic systems
6 Introduction Sensor integration belongs without any doubt to one of the key technologies for the future advancement of robotic systems. In general, we distinguish between: 1. Trajectory-following How can we motions calculate (without a sensors) motion 2. Sensor-guided motions -trajectory Force/torque if we control want a robot to - Visual servo control - react instantaneously to How can we In practice, realize this? unforeseen sensor signals? we need both: 6
7 ICRA
8 ICAR
9 Advanced Robotics
10 10
11 Advanced Robotics
12 12
13 Contents Online Trajectory Generation? Problem and Solution for One Degree of Freedom Extension to Multi-DOF Systems Results 13
14 Input and Output Values Target state of motion at instant Motion constraints at instant Motion state at instant Motion state at instant Type IX VII 14
15 Challenge: Find this function for every single Type! An on-line trajectory generator (OTG) for a system with one degree of freedom is a real function: Overview of all OTG types. 15
16 The Basic Idea There is a finite set of possible motion profiles, of which one transfers one single selected DOF from the initial state of motion to its target state of motion within the shortest possible time (time-optimally).! Velocity profiles Acceleration profiles Jerk profiles 16
17 Challenge: Find this function for every single Type! Overview of all OTG types. 17
18 Type IV OTG Kinematic motion constraints at time instant with - maximum velocity - maximum acceleration - maximum jerk Require (in state space): - current state of motion: - target state of motion: Ensure (in state space): - state of motion at time instant Such that, - is reached in the shortest possible time, and - that the boundary conditions are not breached. Target: 18
19 Reminder: Acceleration Profiles There is a finite set of possible motion profiles, of which one transfers one single selected DOF from the initial state of motion to its target state of motion within the shortest possible time (time-optimally).! Velocity profiles Acceleration profiles Jerk profiles 19
20 Set of all Type IV Acceleration Profiles A system of nonlinear equations can be set up for every acceleration profile. The solution contains all parameters for the calculation of. 20
21 Set of all Type IV Acceleration Profiles Each system of equations is solvable for a proper subset of. The union of all these subsets constitutes the. 21
22 Nonlinear Systems of Equations Two questions: - Which of the systems of equations delivers the desired solution? - How can we calculate, describe, and represent all the borders of each single subset? Decision trees 22
23 Decision Tree 23
24 Decision Tree Input: - current state of motion - target state of motion - kinematic motion constraints Output: - acceleration profile 24
25 Nonlinear Systems of Equations Example: Leads to a system of 12 nonlinear equations with 12 unknowns. 25
26 26 Nonlinear Systems of Equations
27 Position-Error Function (Step 1) 27
28 Derivative of Position-Error Function (Step 1) 28
29 29 Sample Type IV Trajectory for One-DOF
30 30 Sample Result for One DOF (1)
31 31 Sample Result for One DOF (2)
32 32 Solution of the System of Equations
33 Solution of the System of Equations If no (sensor) event happens, the output values from instant are used as input values for instant. Hold element 33
34 34 Solution of the System of Equations
35 Solution of the System of Equations If no (sensor) event happens, the output values from instant are used as input values for instant. Hold element 35
36 36 Solution of the System of Equations
37 Solution of the System of Equations If no (sensor) event happens, the output values from instant are used as input values for instant. Hold element 37
38 38 Solution of the System of Equations
39 Solution of the System of Equations If no (sensor) event happens, the output values from instant are used as input values for instant. Hold element 39
40 40 Solution of the System of Equations
41 is reached after 5340 ms. 41 Solution of the System of Equations
42 Contents Online Trajectory Generation? Problem and Solution for One Degree of Freedom Extension to Multi-DOF Systems Results 42
43 Reminder: The One-Dimensional Case Target state of motion at instant Motion constraints at instant Motion state at instant Motion state at instant Type IX 43
44 Extension to Multi-DOF Systems Vectors with elements Target state of motion at instant Motion constraints at instant Motion state at instant Motion state at instant Type IX VII 44
45 Challenge: Find this function for every single Type! An on-line trajectory generator for a system with multiple degrees of freedom is a real function: Overview of all OTG types. 45
46 Extension to Multi-DOF Systems The resulting motion has to be time-synchronized in all degrees of freedom: - All (position controlled) degrees of freedom reach their target state of motion exactly at the same instant. 46
47 Extension to Multi-DOF Systems The on-line trajectory generation algorithm consists of three steps: Step 1: Step 2: Step 3: Calculate the minimum synchronization time Synchronization of all DOFs to and calculation of all trajectory parameters Calculation of 47
48 Step 1: Calculation of the Synchronization Time Calculation of the minimum execution time for every single DOF: 48
49 Step 1: Calculation of the Synchronization Time But: What would happen here? Type II 49
50 Step 1: Calculation of the Synchronization Time All inoperative time intervals have to be found and calculated. 50
51 Step 1: Calculation of the Synchronization Time Decision trees for the determination of all inoperative time intervals Step 1, Part C. Step 1, Part B. Step 1, Part D. Step 1, Part E. 51
52 Step 2: Synchronization There is a finite set of motion profiles of which one transfers the system's current state of motion to ist desired target state of motion!! This also holds for Step 2. 52
53 Step 2: Synchronization Step 1: - Decision trees: - Set-up and solve systems of equations for each DOF - Determination of the synchronization time Step 2: - Decision trees: - Set-up and solve systems of equations for each DOF - Result: parameters of the desired trajectory 53
54 Step 2: Synchronization 54
55 Step 2: Synchronization Each system of equations is solvable for a proper subset of. Step 1: Step 2: 55
56 Step 2: Synchronization Each system of equations is solvable for a proper subset of. 56
57 Step 2: Synchronization Determination of the system of equations by means of a further decision tree: Step 2. 57
58 Nonlinear Systems of Equations Example: Leads to a system of 14 nonlinear equations with 14 unknowns. 58
59 59 Nonlinear Systems of Equations
60 Position-Error Function (Step 2) 60
61 Position-Error Function (Step 2) 61
62 62 Sample Type IV Trajectory for One-DOF
63 Summary for Type IV Nassi-Shneiderman structogramm for Type IV on-line trajectory generation. 63
64 Further Reading 64
65 Further Reading 65
66 Contents Online Trajectory Generation? Problem and Solution for One Degree of Freedom Extension to Multi-DOF Systems Results 66
67 Arbitrary input values for four DOFs Results 67
68 Sensor-guarded Robot Motions Using a Distance Sensor 68
69 Physical Human-robot Interaction Copyright 2011 Stanford University. 69
70 Simple and Robust Visual Servo Control Copyright 2011 Stanford University. 70
71 Whole-Body Motion Control Copyright 2010 University of Texas at Austin. 71
72 Compliant Manipulation Primitives 72
73 Whole-Body Motion Control Copyright 2011 Stanford University. 73
74 Whole-Body Motion Control 74
75 Whole-Body Motion Control Copyright 2011 Stanford University. 75
76 ...not only walk, but also interact with the world... 76
77 ...not only walk, but also interact with the world... Copyright 2011 Stanford University. 77
78 The Reflexxes Motion Libraries Target-position-based Library (Type IV) 78
79 The Reflexxes Motion Libraries Target-velocity-based Library (Type IV) 79
80 Schedule 8:30-10:00 Introduction and basics 10:00-10:30 Coffee break 10:30-11:30 Reflexxes API Programming examples 11:30-11:45 Coffee break 11:45-12:30 Application examples Research and outlook 80
81 Reflexxes API 81
82 82
83 Programming Examples 83
84 84
85 Schedule 8:30-10:00 Introduction and basics 10:00-10:30 Coffee break 10:30-11:30 Reflexxes API Programming examples 11:30-11:45 Coffee break 11:45-12:30 Application examples Research and outlook 85
86 Application Examples 86
87 State of the Art in Technology Servo Drive Control No online synchronization with jerk-limitation for multi-axis systems 87
88 State of the Art in Research Robotics No online trajectory generation approach that - copes with arbitrary initial states - provides jerk-limited motions - considers the current dynamics 88
89 The Reflexxes Motion Libraries Motion generation in less than one millisecond. Instantaneous reactions to unforeseen sensor signals and events 89
90 Contents JediBot Visual servo control Hybrid switched-system control Playing Jenga 90
91 JediBot Copyright 2011 Stanford University. 91
92 Components 92
93 Visual Perception Copyright 2011 Stanford University. 93
94 Visual Perception Procedure 1) Filter on depth and color 2) RANSAC stick fitting 3) Extract sword end points 4) Filter on sword length Copyright 2011 Stanford University. 94
95 Defense Mode Computation of the defense point at ~15 Hz During the defense mode, the camera is part of the feedback control loop. The Reflexxes Motion Library assures continuous executable trajectories. 95
96 Attack and Contact Modes Perform random attack motion towards the opponent Joint torque sensors to detect contact After contact: switch back to contact strategy (and recoil) 96
97 Four Different Control Strategies Defense: Block attack motions of the opponent Attack: Execute one attack motion towards the opponent Contact: Instantaneously recoil Hover: No opponent detected Selection variable Target state 97
98 Hybrid Switched-system Control 98
99 Attack and Contact Modes 99
100 Defense Mode 100
101 Results Sample trajectory with mode switchings 101
102 Contents JediBot Visual servo control Hybrid switched-system control Playing Jenga 102
103 Control Scheme 103
104 Important Features Guaranteed continuity and jerk limitation Position Velocity Acceleration Constraints 104
105 Results 105
106 Results 106
107 Image Processing and Robustness Output of the vision system Continuous motion in case of - outliers - insufficient image quality - obstacles in front of the camera - camera failures - misbehavior of the image processing system Physical & artificial workspace limitations 107
108 Results 108
109 Contents JediBot Visual servo control Hybrid switched-system control Playing Jenga 109
110 Introduction and Motivation Simplified hybrid switched-control scheme a for one-dof system: State of motion: 110
111 Problem Issues Force/torque control - What happens if a stable contact cannot be established? - How do we safely react to sensor failures? Visual servo control - What happen if no valid motion signal can be generated? - What happens if a camera is covered by an obstacle, or how can we safely react to camera failures? General instability issues - How do we react after inappropriate switching procedures? - How do we react to incorrect/wrong task parameters? - How do we react if control submodules were chosen incorrectly? 111
112 Introduction and Motivation Simplified hybrid switched-control scheme a for one-dof system: Particularity: The two OTG modules can take over control at any time. 112
113 Detecting an Unstable System Switching rate too high Amplitude exceeds maximum value A motion state variable transformed to the frequency domain is greater than a certain frequency Sensor value out of range Robot system tends to leave its workspace or heads towards a singularity during a sensor-guided motion Maximum actuator forces or torques reached Sensor malfunctions 113
114 Stabilizing hybrid switched-systems (velocity target) Velocity-acceleration plane in state space: ICRA
115 Stabilizing hybrid switched-systems Velocity-acceleration plane in state space: ICRA
116 Unforeseen Switching of Reference Frames 116
117 Unforeseen Switching of State Spaces 117
118 Instantaneous Controller Switching Copyright 2010 Stanford University. 118
119 Contents JediBot Visual servo control Hybrid switched-system control Playing Jenga 119
120 Manipulation Primitives Selection Matrix classical selection matrix adaptive selection matrix dof x y z level dof x y z x x y y z z Position Velocity Distance Force/Torque Further device Position Velocity Distance Force/Torque Further device An example: Level 0 Level 1 Level 2 Force in z-direction Force Vision Velocity 120
121 Schnittstelle zur Bewegungsplanung 121 Hybrid Switched-System Control
122 Playing Jenga! 122 ICRA 2006
123 Research and Outlook 123
124 Contents ROS and MoveIt! Integrating dynamic models Human-robot collision avoidance Highly responsive proximity sensing 124
125 ROS and MoveIt! Copyright 2011 Stanford University. 125
126 ROS and MoveIt! Automatically computing intermediate motion states 126
127 Contents ROS and MoveIt! Integrating dynamic models Human-robot collision avoidance Highly responsive proximity sensing 127
128 Integrating Dynamic Models Copyright 2013 Stanford University. 128
129 Contents ROS and MoveIt! Integrating dynamic models Human-robot collision avoidance Highly responsive proximity sensing 129
130 Human-robot Collision Avoidance End effector repulsive vector repulsive velocity Collision avoidance for the robot body Repulsive vector Cartesian constraints Joint velocity limit Smooth, jerk limited motions feeling of safety 130
131 Safe Coexistence Collision avoidance in depth space 131
132 Human-robot Collision Avoidance Collision avoidance algorithm, which : is directly used in depth space deploys real sensors (not hypothetic) considers multiple obstacles whole robot body uses obstacle motions for prediction (fast) benefits from Reflexxes framework (smooth motions, instantaneous reactions) runs in real-time 132
133 Contents ROS and MoveIt! Integrating dynamic models Human-robot collision avoidance Highly responsive proximity sensing 133
134 Highly Responsive Proximity Sensing 134
135 Schedule 8:30-10:00 Introduction and basics 10:00-10:30 Coffee break 10:30-11:30 Reflexxes API Programming examples 11:30-11:45 Coffee break 11:45-12:30 Application examples Research and outlook 135
136 Thank You! Acknowledgements Fabrizio Flacco Jose Padial Andre Gaschler Thomas Schlegl Christian Hurnaus Adam Tomiczek Robert Katzschmann Friedrich Wahl Oussama Khatib Taizo Yoshikawa Ken Oslund 136
137 Thank You Very Much for Your Attention! Enjoy ICRA 2013 and your stay in Karlsruhe...! 137
138 ICRA Tutorial, May 6, 2013 The Reflexxes Motion Libraries An Introduction to Instantaneous Trajectory Generation Torsten Kroeger 138
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