COPRIN project. Contraintes, OPtimisation et Résolution par INtervalles. Constraints, OPtimization and Resolving through INtervals. 1/15. p.

Transcription

1 COPRIN project Contraintes, OPtimisation et Résolution par INtervalles Constraints, OPtimization and Resolving through INtervals 1/15. p.1/15

2 COPRIN project Contraintes, OPtimisation et Résolution par INtervalles Constraints, OPtimization and Resolving through INtervals COPRIN has been created in February /15. p.1/15

3 Members of the project Staff MERLET Jean-Pierre (DR 1, scientific head) DANEY David (Chargé de Recherche INRIA) NEVEU Bertrand (Ingénieur en Chef, P & C, CERTIS) PAPEGAY Yves (Chargé de Recherche INRIA) POURTALLIER Odile (Chargé de Recherche INRIA, join the team in 2004) TROMBETTONI Gilles (Maître de Conférences UNSA) Students 7 PhD students 1 post-doc 1 engineer 2/15. p.2/15

4 Scientific objectives and Methods 3/15. p.3/15

5 Scientific objectives and Methods Two main complementary research axis: Robotics and Interval Analysis 3/15. p.3/15

6 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis 3/15. p.3/15

7 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis establishing the performances of a given robot 3/15. p.3/15

8 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis establishing the performances of a given robot in a guaranteed manner 3/15. p.3/15

9 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis establishing the performances of a given robot in a guaranteed manner especially taking into account the uncertainties in the modeling and control 3/15. p.3/15

10 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis Robotics Objective 2: design methodology 3/15. p.3/15

11 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis Robotics Objective 2: design methodology establishing the robot design parameters so that it will fit given requirements 3/15. p.3/15

12 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis Robotics Objective 2: design methodology establishing the robot design parameters so that it will fit given requirements methodology provides almost all design solutions 3/15. p.3/15

13 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis Robotics Objective 2: design methodology establishing the robot design parameters so that it will fit given requirements methodology provides almost all design solutions methodology is robust with respect to manufacturing tolerances 3/15. p.3/15

14 Scientific objectives and Methods Robotics Robotics Objective 1: robot modeling and analysis Robotics Objective 2: design methodology Robotics Objective 3: parallel robot, prototypes, applications 3/15. p.3/15

15 Example: new wire-driven parallel robot 4/15. p.4/15

16 Example: new wire-driven parallel robot Highly modular 4/15. p.4/15

17 Example: new wire-driven parallel robot Highly modular Linear actuators 4/15. p.4/15

18 Example: new wire-driven parallel robot Highly modular Linear actuators Applications: service robotics rehabilitation 4/15. p.4/15

19 Scientific objectives and Methods 5/15. p.5/15

20 Scientific objectives and Methods Interval Analysis/Constraints certified solving 5/15. p.5/15

21 Scientific objectives and Methods Interval Analysis/Constraints certified solving of equations and/or inequalities systems 5/15. p.5/15

22 Scientific objectives and Methods Interval Analysis/Constraints certified solving of equations and/or inequalities systems for real variables, lying in a bounded domain 5/15. p.5/15

23 Scientific objectives and Methods Interval Analysis/Constraints certified solving of equations and/or inequalities systems for real variables, lying in a bounded domain providing results that are guaranteed 5/15. p.5/15

24 Scientific objectives and Methods Interval Analysis/Constraints certified solving methods: 5/15. p.5/15

25 Scientific objectives and Methods Interval Analysis/Constraints certified solving methods: constraint programming interval analysis symbolic computation 5/15. p.5/15

26 Interval analysis 6/15. p.6/15

27 Interval analysis Calculating with intervals is (almost) as easy than with real numbers 6/15. p.6/15

28 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] 6/15. p.6/15

29 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) 6/15. p.6/15

30 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) 6/15. p.6/15

31 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0, 1] + cos([0, 1]) 6/15. p.6/15

32 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0, 1] + cos([0, 1]) 6/15. p.6/15

33 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0, 1] + [0.54, 1] 6/15. p.6/15

34 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0,1]+[0.54,1] 6/15. p.6/15

35 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0,1]+[0.54,1] = [0.54,2] 6/15. p.6/15

36 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0,1]+[0.54,1] = [0.54,2] 0 not included in [0.54,2] F 0 x [0, 1] 6/15. p.6/15

37 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0,1]+[0.54,1] = [0.54,2] 0 not included in [0.54,2] F 0 x [0, 1] F > 0 x [0, 1] 6/15. p.6/15

38 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0,1]+[0.54,1] = [0.54,2] Advantages:numerical round-off errors are managed 6/15. p.6/15

39 Interval analysis Calculating with intervals is (almost) as easy than with real numbers Example: F = x 2 + cos(x), x [0, 1] Problem: find [A,B] such that: A F(x) B x [0, 1] F = [0, 1] 2 + cos([0, 1]) = [0,1]+[0.54,1] = [0.54,2] Advantages:numerical round-off errors are managed Drawbacks: overestimation, calculation sensitive to formulation 6/15. p.6/15

40 The structure of an IA algorithm 7/15. p.7/15

41 The structure of an IA algorithm... A list of boxes 7/15. p.7/15

42 The structure of an IA algorithm Filtering operator 7/15. p.7/15

43 The structure of an IA algorithm Filtering operator Filtering operator: a set of heuristics that may allow to determine that there is no solution in the current box or may reduce its size 7/15. p.7/15

44 The structure of an IA algorithm Filtering operator Existence operator 7/15. p.7/15

45 The structure of an IA algorithm Filtering operator Existence operator Existence operator: a set of heuristics that may allow to determine that there is a single solution in the current box (e.g Kantorovitch theorem) 7/15. p.7/15

46 The structure of an IA algorithm Filtering operator Existence operator Bisection 7/15. p.7/15

47 The structure of an IA algorithm Filtering operator Existence operator Bisection Split the current box, usually in two 7/15. p.7/15

48 The structure of an IA algorithm Filtering operator Existence operator Bisection 7/15. p.7/15

49 The structure of an IA algorithm Filtering operator Existence operator Bisection 7/15. p.7/15

50 An example 8/15. p.8/15

51 An example Managing a set of inequalities: x 2 + y 2 2 (x 1) 2 + (y 1) 2 2 that play a role in the calculation of a parallel robot workspace VIDEO 8/15. p.8/15

52 Interval Analysis Objectives 9/15. p.9/15

53 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology 9/15. p.9/15

54 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology new filtering operators 9/15. p.9/15

55 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology new filtering operators decomposition and solving of geometric constraints 9/15. p.9/15

56 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology new filtering operators decomposition and solving of geometric constraints solving of differential equations 9/15. p.9/15

57 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology IA Objective 2: Dissemination, software, experimental analysis 9/15. p.9/15

58 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology IA Objective 2: Dissemination, software, experimental analysis method is not well known 9/15. p.9/15

59 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology IA Objective 2: Dissemination, software, experimental analysis method is not well known lack of available software 9/15. p.9/15

60 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology IA Objective 2: Dissemination, software, experimental analysis method is not well known lack of available software interface not convenient for non expert end-user 9/15. p.9/15

61 Interval Analysis Objectives IA Objective 1: Improvement of IA methodology IA Objective 2: Dissemination, software, experimental analysis Tools: extensive use of symbolic computation software (ALIAS library) extensive testing 9/15. p.9/15

62 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) 10/15. p.10/15

63 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) robot 10/15. p.10/15

64 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) R2 R1 robot 10/15. p.10/15

65 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) R2 R1 robot 10/15. p.10/15

66 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) R2 R1 robot 10/15. p.10/15

67 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) R2 R1 robot R2 receives the ping at time t 2 10/15. p.10/15

68 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) R2 R1 robot 10/15. p.10/15

69 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) R2 R1 robot R1 receives the ping at time t 1 10/15. p.10/15

70 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) Localization is based on the measurement of t 2 t 1 With 2 receivers: assuming perfect Dirac ping RR 2 RR 1 = c(t 2 t 1 ) robot lie on a hyperbola 10/15. p.10/15

71 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) Localization is based on the measurement of t 2 t 1 With 2 receivers: assuming perfect Dirac ping: RR 2 RR 1 = c(t 2 t 1 ) robot lie on a hyperbola In practice we have sinusoidal ping: measured time is an interval robot lie on a "thick" hyperbola 10/15. p.10/15

72 Localization with ultra-sound Localization of a robot with ultra-sound (joint work with ETH) With three receivers measurement of t 2 t 1,t 3 t 1 robot located at the intersection of 2 "thick" hyperbola 10/15. p.10/15

73 Analysis 11/15. p.11/15

74 Analysis Usually f,c are assumed to be perfectly known 11/15. p.11/15

75 Analysis but in practice f, c are uncertain c in [1465,1496] m/s (±5degrees temperature variation) f in [295,305] khz Influence of these uncertainties on the robot localization? 11/15. p.11/15

76 Analysis but in practice f, c are uncertain c in [1465,1496] m/s (±5degrees temperature variation) f in [295,305] khz Influence of these uncertainties on the robot localization? robot location discarding uncertainties possible real location 11/15. p.11/15

77 Synthesis 12/15. p.12/15

78 Synthesis not satisfied with the localization accuracy? find the location of the 3rd receiver so that the localization accuracy is lower than a given threshold 12/15. p.12/15

79 Synthesis not satisfied with the localization accuracy? find the location of the 3rd receiver so that the localization accuracy is lower than a given threshold IA methods allows to find all 3rd receiver location that allow to respect this requirement 12/15. p.12/15

80 Synthesis /15. p.12/15

81 Synthesis this methodology allows to design robots that fit a list of requirements it has been used for designing industrial robots and our own prototypes 12/15. p.12/15

82 achine-tool (CMW) Fine positioning (ESRF) Space telescope (Alcatel) 1 mètre 12/15. p.12/15

83 MIPS micro robot ARES micro-robot wire robot this methodology is used to manage the modularity of our wire-driven parallel robot find the geometry that allows to lift an elderly people whatever his/her location in a given room 12/15. p.12/15

84 Wire-driven parallel robot 13/15. p.13/15

85 Wire-driven parallel robot All purpose device with 1 to 6 d.o.f., redundant or not highly modular: geometry, amplification of actuator motion powerful: high ratio load/mass fast: potentially faster than the speed of sound Examples: 4 dof crane motion video, fast planar motion (3.5m/s) 13/15. p.13/15

86 Wire-driven parallel robot Potential applications: domestic robotics: windows washing 13/15. p.13/15

87 Wire-driven parallel robot Potential applications: domestic robotics: windows washing entertainment: actor motion in theater, fast change in scenes 13/15. p.13/15

88 Wire-driven parallel robot Potential applications: domestic robotics: windows washing entertainment: actor motion in theater, fast change in scenes catastrophe: portable multi-dof crane (ADT) 13/15. p.13/15

89 Wire-driven parallel robot Potential applications: domestic robotics: windows washing entertainment: actor motion in theater, fast change in scenes catastrophe: portable multi-dof crane (ADT) haptic interface: virtual reality, training with force-feedback 13/15. p.13/15

90 Wire-driven parallel robot Potential applications: domestic robotics: windows washing entertainment: actor motion in theater, fast change in scenes catastrophe: portable multi-dof crane (ADT) haptic interface: virtual reality, training with force-feedback assistance robotics: lifting of elderly people (lifting video) 13/15. p.13/15

91 Wire-driven parallel robot Potential applications: domestic robotics: windows washing entertainment: actor motion in theater, fast change in scenes catastrophe: portable multi-dof crane (ADT) haptic interface: virtual reality, training with force-feedback assistance robotics: lifting of elderly people (lifting video) rehabilitation 13/15. p.13/15

92 Example: rehabilitation 14/15. p.14/15

93 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke 14/15. p.14/15

94 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Classical rehabilitation training: arm pointing to colored marks moving randomly on a computer screen 14/15. p.14/15

95 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Classical rehabilitation training: arm pointing to colored marks moving randomly on a computer screen Drawbacks: no monitoring of the arm motion 14/15. p.14/15

96 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Classical rehabilitation training: arm pointing to colored marks moving randomly on a computer screen Drawbacks: no monitoring of the arm motion no objective mean to qualify the motion quality 14/15. p.14/15

97 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Classical rehabilitation training: arm pointing to colored marks moving randomly on a computer screen Drawbacks: no monitoring of the arm motion no objective mean to qualify the motion quality fatigue induced by pointing the arm 14/15. p.14/15

98 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Robot assisted rehabilitation 14/15. p.14/15

99 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Robot assisted rehabilitation use trajectory tracking to monitor and qualify motions 14/15. p.14/15

100 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Robot assisted rehabilitation use trajectory tracking to monitor and qualify motions relieve partly arm gravity for focusing on coordination 14/15. p.14/15

101 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Robot assisted rehabilitation: (rehabilitation video) 14/15. p.14/15

102 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Robot assisted rehabilitation: (rehabilitation video) gravity effects decreased by 50% 14/15. p.14/15

103 Example: rehabilitation Patient suffering from loss of arm coordination after a cardiovascular stroke Robot assisted rehabilitation: (rehabilitation video) gravity effects decreased by 50% trajectory tracking: straightness of the trajectory allows to qualify motion quality 14/15. p.14/15

104 Example: rehabilitation Trajectory tracking 14/15. p.14/15

105 Recent objectives 15/15. p.15/15

106 Recent objectives Focus on service robotics 15/15. p.15/15

107 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices 15/15. p.15/15

108 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) 15/15. p.15/15

109 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding 15/15. p.15/15

110 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding developing various interfaces to manage the end-user abilities 15/15. p.15/15

111 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding developing various interfaces to manage the end-user abilities low intrusivity: use already accepted objects, systems are invisible if not in use 15/15. p.15/15

112 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding developing various interfaces to manage the end-user abilities low intrusivity: use already accepted objects, systems are invisible if not in use provide information for doctors: early detection of emerging pathologies 15/15. p.15/15

113 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding developing various interfaces to manage the end-user abilities low intrusivity: use already accepted objects, systems are invisible if not in use provide information for doctors: early detection of emerging pathologies safety: improve emergency detection, prevent fall 15/15. p.15/15

114 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding developing various interfaces to manage the end-user abilities low intrusivity: use already accepted objects, systems are invisible if not in use provide information for doctors: early detection of emerging pathologies safety: improve emergency detection, prevent fall smart device: communicating devices, using all types of media (hertzian, IR, optical,... ) 15/15. p.15/15

115 Recent objectives Focus on service robotics developing various low-cost assistance robotized devices user-centered (systematic collaboration with end-users) developing methodologies to adapt the device to the end-user and its surrounding developing various interfaces to manage the end-user abilities low intrusivity: use already accepted objects, systems are invisible if not in use provide information for doctors: early detection of emerging pathologies safety: improve emergency detection, prevent fall smart device: communicating devices, using all types of media (hertzian, IR, optical,... ) active participation to the large scale initiative PAL (Personally Assisted Living) Example: assistance for elderly people (video) 15/15. p.15/15