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Contrôle de la locomotion artificielle: Une approche par commande prédictive sans trajectoire de référence Philippe Poignet (LIRMM, Montpellier) Christine.

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Presentation on theme: "Contrôle de la locomotion artificielle: Une approche par commande prédictive sans trajectoire de référence Philippe Poignet (LIRMM, Montpellier) Christine."— Presentation transcript:

1 Contrôle de la locomotion artificielle: Une approche par commande prédictive sans trajectoire de référence Philippe Poignet (LIRMM, Montpellier) Christine Azevedo (INRIA, Grenoble)

2 2 Context | Human locomotion features | Control approach | Conclusions & perspectives Context 1. Biped robots 2. Locomotion control 3. Guidelines of the research

3 3 ASIMO & P3 Honda Motor Co Wabian Waseda University M2 MIT Johnnie TUM Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Some realisations 1. Biped robots

4 Mobility environment perception & understanding adaptation autonomy Biped stability skills (contacts, impacts) robustness to disturbances falls paradigms 2. General issues 1. Biped robots 4 Context | Human locomotion features | Control approach | Conclusions & perspectives Mobile robots: wheeled, caterpillar, legged Legged robots: n-legs, biped cluttered environments human facilities (stairs, corridors…)

5 - trunk + pelvis + 2 legs - 15 active joints: 7 sagittal: ankles, knees, hips, trunk 5 frontal: ankles, hips, trunk 3 horizontal: hips, trunk - 105 kg - 180 cm - human proportions BIP was designed and built in collaboration between INRIA and LMS Poitiers 1. Biped robots 5 Context | Human locomotion features | Control approach | Conclusions & perspectives 3. BIP: the anthropomorphic robot

6 6 Context | Human locomotion features | Control approach | Conclusions & perspectives Context 1. Biped robots 2. Locomotion control 3. Guidelines of the research

7 7 Pre-computed reference trajectory tracking - anthropomorphic joint trajectories [vukobratovic et al 01] - torque trajectories [goswami et al 96], [pratt & pratt et al 01] - - optimal trajectories [chevallereau et al 97], [chessé & bessonnet 01] Pre-computed movements non-adaptable to environment and events changes Context | Human locomotion features | Control approach | Conclusions & perspectives 1. State of the art Control Reference trajectories Desired behaviourReal behaviour Sensors information 2. Locomotion control

8 8 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Locomotion control 1. State of the art (2) On-line walking adaptation - - ZMP compensation [park99] - - discrete set of trajectories [denk01] [ large set of trajectories needed + switches - continuous set of parameterized trajectories [wieber00][chevallereau02] defining the set - learning techniques [kun96] - neuro-fuzzy [meyret02] no explicit model

9 9 Context | Human locomotion features | Control approach | Conclusions & perspectives Context 1. Biped robots 2. Locomotion control 3. Guidelines of the research

10 11 1. no trajectory tracking + 2. high adaptability + no algorithm switches 3. robustness to disturbances searching inspiration from human walking without mimicking Context | Human locomotion features | Control approach | Conclusions & perspectives Control Reference trajectories Desired behaviourReal behaviour Sensors information New approach to biped locomotion control

11 12 1. Locomotion structure (biomechanics) 2. Locomotion control (neurosciences) 3. Conclusion : some principles Human locomotion features Context | Human locomotion features | Control approach | Conclusions & perspectives

12 13 1. 1.stationary / transient gait (stop, starting,…) 2. 2.stationary walk: symmetric + cyclic 3. 3.phases :support and swing 4. 4.supports: single support and double support 5. 5.variable patterns (tiredness, learning…) 6. 6.objective oriented optimization of displacements (metabolic energy minimization in stationary walk) [vaughan et al 92] Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Locomotion structure 1. Walking activity

13 14 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Locomotion structure 2. Equilibrium Static equilibrium: CoM projection within support base (posture, difficult situations, working at a work station…) Dynamic equilibrium: normal walking fall forward onto the foot receiving the bodys weight. Definition remains an open problem for bipedal systems with unilateral constraints.

14 15 1. Locomotion structure (biomechanics) 2. Locomotion control (neurosciences) 3. Conclusion : some principles Human locomotion features Context | Human locomotion features | Control approach | Conclusions & perspectives

15 2. Locomotion control 1. Control process muscles actuators muscles actuators skeleton system skeleton system Sensors CNS controller CNS controller intention activationforce movement environment disturbances 16

16 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Locomotion control 1. Control process muscles actuators muscles actuators skeleton system skeleton system Sensors CNS controller CNS controller intention activationforce movement environment disturbances 16 2. Control properties - - No reference trajectory tracking - - Anticipation and prediction: CNS internal models planning - - Strategy: library of objective oriented solutions - - Learning: taking lessons from past situations

17 17 1. Locomotion structure (biomechanics) 2. Locomotion control (neurosciences) 3. Conclusion : some principles Human locomotion features Context | Human locomotion features | Control approach | Conclusions & perspectives

18 18 Unsuccessful approaches in exploiting movements invariants. 1. Locomotion structure - Consider both stationary and transient walk - Optimal gaits / criteria adapted to goal (endurance, speed) - Consider both static and dynamic equilibrium 2. Locomotion control - No reference trajectory tracking - Perception - Anticipation and prediction - Consider internal and external constraints to ensure feasibility and equilibrium. Context | Human locomotion features | Control approach | Conclusions & perspectives 3. Conclusion: some principles idea: use a model predictive control approach

19 19 1. Modelling 2. Model predictive control 3. Application of MPC to locomotion control 4. Simulation results 5. Conclusions Control approach Context | Human locomotion features | Control approach | Conclusions & perspectives Use of a model predictive control (MPC) approach:

20 20 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics q7q7 q8q8 joint positions robot orientation and position in 3D space 1. Lagrange formulation [wieber00] [genot98] [pfeiffer96] Depending on the contacts the system can be underactuated n dof

21 21 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (1) 1. Lagrange formulation 2. Ground contact =( n, t ) T n t support force

22 21 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (1) 1. Lagrange formulation 2. Ground contact closure constraint: =( n, t ) T n t support force

23 22 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (2) =( n, t ) T n t

24 22 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (2) unilateral constraint =( n, t ) T n t

25 22 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (2) unilateral constraint =( n, t ) T n t

26 22 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (2) unilateral constraint complementarity condition =( n, t ) T n t

27 22 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 1. Continuous dynamics (2) unilateral constraint complementarity condition no-slipping assumption (friction cone ) =( n, t ) T n t

28 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics

29 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics Impact velocity jump: =( n, t ) T

30 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics Impact velocity jump: n t =( n, t ) T Impulsive force

31 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics Impact velocity jump: n t =( n, t ) T

32 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics Impact velocity jump: no take-off assumption n t =( n, t ) T

33 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics Impact velocity jump: no-slipping assumption (friction cone ) no take-off assumption n t =( n, t ) T

34 23 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. Modelling 2. Impact dynamics Impact velocity jump: no-slipping assumption (friction cone ) no take-off assumption n t =( n, t ) T

35 24 1. Modelling 2. Model predictive control 3. Application of MPC to locomotion control 4. Simulation results 5. Conclusions Control approach Context | Human locomotion features | Control approach | Conclusions & perspectives Use of a model predictive control (MPC) approach:

36 25 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 1. Control without predictive horizon

37 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k 2. Model predictive control 1. Control without predictive horizon

38 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

39 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

40 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

41 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 k+2 ? Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

42 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 k+2 Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

43 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 k+2 ? Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

44 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k+1 k+2 Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

45 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k+1 k+2 ? Obstacle detection Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

46 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k+2 k+3 ? Obstacle Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

47 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? Obstacle Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

48 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state Obstacle ? Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

49 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state Obstacle ? Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

50 25 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state Obstacle ? No solution !!! Example: elevation of the swing ankle 2. Model predictive control 1. Control without predictive horizon

51 26 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Control with predictive horizon 2. Model predictive control

52 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

53 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

54 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state k k+1 k+N c Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

55 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? k k+1 k+N c Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

56 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? k k+1 k+N c Obstacle detection Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

57 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? k k+1 k+N c Obstacle detection Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

58 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? k k+1 k+N c Obstacle detection Example: elevation of the swing ankle sliding horizon 2. Model predictive control 2. Control with predictive horizon

59 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? k+1 k+N c +1 Obstacle detection Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

60 26 Context | Human locomotion features | Control approach | Conclusions & perspectives time input state ? Obstacle detection k+1 k+2 k+N c +2 Example: elevation of the swing ankle 2. Model predictive control 2. Control with predictive horizon

61 27 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 3. Description

62 27 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 3. Description Control horizon time k k+1 k+N c k+N p Predictive horizon

63 28 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 4. Formal problem

64 28 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 4. Formal problem with: [allgöwer99]

65 28 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 4. Formal problem with: function of input and state (trajectory tracking or regulation) [allgöwer99] control horizon predictive horizon

66 29 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 5. State of the art

67 29 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Model predictive control 5. State of the art Linear systems: - Widely used in linear slow systems (GPC, PFC) [richalet93] - Many stability proofs results [garcia89][boucher96][rawlings93] Nonlinear systems: - Usually used in slow systems - Stability proofs / strong assumptions: infinite horizon [mayne90][meadow93], dual mode [michalska93][chisci96], terminal equality constraint [chen82][alamir94], quasi infinite horizon [garcia89][denicolao97]

68 30 1. Modelling 2. Model predictive control 3. Application of MPC to locomotion control 4. Simulation results 5. Conclusions Control approach Context | Human locomotion features | Control approach | Conclusions & perspectives Use of a model predictive control (MPC) approach:

69 31 Context | Human locomotion features | Control approach | Conclusions & perspectives 3. Application of MPC to locomotion control 1. Problem N c =N p function of input and state (trajectory tracking or regulation)

70 32 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. From human observation to problem specification 3. Application of MPC to locomotion control

71 32 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. From human observation to problem specification 3. Application of MPC to locomotion control Walking = shift the body in a standing posture without falling 1) 1)Criteria: gait optimization / objective of the walk 2) 2)Constraints i) Standing posture maintain the CoM height ii) Locomotion rhythm forward moving of CoM iii) static/dynamic equilibrium contact forces control iv) adaptation to environment ground and obstacle avoidance i inequality constraints expressions ? [hurmuzlu93]

72 33 Context | Human locomotion features | Control approach | Conclusions & perspectives 3. Example of criteria and constraints specification 3. Application of MPC to locomotion control

73 33 Context | Human locomotion features | Control approach | Conclusions & perspectives 3. Example of criteria and constraints specification 3. Application of MPC to locomotion control Criteria: Constraints: 1) Dynamics: continuous + impacts 2) Actuator limits : 3) Joint limits: 4) Standing posture: 5) Forward progression: 6) Ground avoidance: 7) Dynamic balance: Expressed in output space

74 34 1. Modelling 2. Model predictive control 3. Application of MPC to locomotion control 4. Some simulation results 5. Conclusions Control approach Context | Human locomotion features | Control approach | Conclusions & perspectives Use of a model predictive control (MPC) approach:

75 35 Context | Human locomotion features | Control approach | Conclusions & perspectives 4. Some simulation results Different simulation results have been tested, 3 of them are presented here: 1. One dynamic step with BIP 2. Static walk on flat ground and stairs 3. Dynamic steps with RABBIT Simulation conditions: sagittal plane sampling period: 10 ms algorithm: SQP software: matlab

76 36 Context | Human locomotion features | Control approach | Conclusions & perspectives 4. Some simulation results 1. One dynamic step 2D Dynamic walking BIP - 6 actuators – 9 dof N c =3.Te= 30 ms

77 37 Context | Human locomotion features | Control approach | Conclusions & perspectives 4. Some simulation results 1. One dynamic step 2D Dynamic walking BIP - 6 actuators – 9 dof N c =3.Te= 30 ms

78 38 Context | Human locomotion features | Control approach | Conclusions & perspectives 1. One dynamic step 2D Dynamic walking BIP - 6 actuators – 9 dof 4. Some simulation results N c =3.Te= 30 ms

79 39 Context | Human locomotion features | Control approach | Conclusions & perspectives 2. Auto-adaptation to environment 2D Static walking BIP - 6 actuators – 6 dof 4. Some simulation results N c =5.Te= 50 ms

80 40 Context | Human locomotion features | Control approach | Conclusions & perspectives 3. Application to an under actuated robot structure 2D Dynamic walking RABBIT – 4 actuators – 7dof 4. Some simulation results N c =3.Te= 30 ms

81 41 Context | Human locomotion features | Control approach | Conclusions & perspectives 5. Conclusions Exploration of a new approach to robot dynamic walking: MPC + constraints + no reference trajectory generation and tracking + auto-adaptation to environment changes (no switches) + integration of internal and external constraints + adaptable to different robots structures - computation times - stability definition and proof - walking activity translation into inequality constraints


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