Simulation based analysis of human push recovery motions using - PowerPoint PPT Presentation

, Simulation based analysis of human push recovery motions using numerical optimization malin.schemschat@iwr.uni-heidelberg.de September 1, 2016 malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 0 / 21

Motivation , adult eldery young stable gait, → more likely → often fall → reaction on to fall perturbation malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 1 / 21

Application , Shape Robotics Humanoids Control Exoskeletons Strategies Medicine Prostheses Therapies Sport Science Training malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 2 / 21

Workflow , Experiments Optimal Control Human Problem Motion (OCP) Dynamic Model x = f ( t , x , u , p ) ˙ malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 3 / 21

Human Model , 2D human model. 14 segments connected by 13 joints (+3D joint for position and orientation in world coordinates). Rotations around y-axis in sagittal plane. Controlled by joint torques. Push simulated as external force. Implemented based on HeiMan in RBDL 1 . Height: 1 . 80 m, weight: 75 kg 1 M.L. Felis. RBDL - an efficient rigid-body dynamics library using recursive algorithms. Autonomous Robots, 2015. malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 4 / 21

Modeling , Equations of motion Dynamics of model during a phase described by equations of motion + G ( q ) T λ = M ( q )¨ τ (¨ q , ˙ q , q ) q + C ( q , ˙ q ) q pelvis position and orientation and joint angles, q corresponding velocities, ¨ ˙ q accelerations, τ joint torques, λ external impact forces resulting from a contact, G Jacobi Matrix of the constraints, M inertia term, C amount of forces to be applied to enforce acceleration ¨ q to be zero, malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 5 / 21

Modeling , Equations of motion Dynamics of model during a phase described by equations of motion push f push + G ( q ) T λ = M ( q )¨ T τ (¨ q , ˙ q , q ) + G q + C ( q , ˙ q ) q pelvis position and orientation and joint angles, q corresponding velocities, ¨ ˙ q accelerations, τ joint torques, λ external impact forces resulting from a contact, G Jacobi Matrix of the constraints, M inertia term, C amount of forces to be applied to enforce acceleration ¨ q to be zero, G push Jacobian of push point, f push applied force. malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 5 / 21

Modeling , Equations of motion Dynamics of model during a phase described by equations of motion push f push + G ( q ) T λ = M ( q )¨ T τ (¨ q , ˙ q + C ( q , ˙ q , q ) + G q ) (1) q and λ ∈ R m → Reformulation to linear system with unknowns ¨ � � ¨ G T T � � � − C + τ + G � M q push f push = . (2) − ˙ G 0 − λ G ˙ q → Reformulation of linear system (2) to DAE of first order ˙ x = f ( t , x , u , p ) , (3) where x = ( q , ˙ q ), u = τ . malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 6 / 21

Optimization , Optimal Control Problem min J ( t , x ( t ) , u ( t ) , p ) objective function x , u , p , t 0 ,..., t nph  x ( t ) = f j ( t , x ( t ) , u ( t ) , p ) , ˙ equation of motion    g j ( t , x ( t ) , u ( t ) , p ) ≥ 0 , path constraints  s.t.    t 0 = 0 , t n ph = t f , t ∈ [ t j − 1 ; t j ] .  x = ( q , ˙ q ) system state variables, u = τ system control variables, p system parameters. malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 7 / 21

Optimization , Optimal Control Problem min J ( t , x ( t ) , u ( t ) , p ) objective function x , u , p , t 0 ,..., t nph  x ( t ) = f j ( t , x ( t ) , u ( t ) , p ) , ˙ equation of motion    g j ( t , x ( t ) , u ( t ) , p ) ≥ 0 , path constraints  s.t.    t 0 = 0 , t n ph = t f , t ∈ [ t j − 1 ; t j ] .  Contact Phase 1 Phase 2 Phase 3 Phase 4 right hallux yes yes yes yes right heel yes no no no left hallux start no no yes left heel no no yes yes malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 8 / 21

Optimization , Motion generation min J ( t , x ( t ) , u ( t ) , p ) objective function x , u , p , t 0 ,..., t nph  x ( t ) = f j ( t , x ( t ) , u ( t ) , p ) , ˙ equation of motion    g j ( t , x ( t ) , u ( t ) , p ) ≥ 0 , path constraints  s.t. r ( x ( t 0 ) , x ( t 1 ) , . . . , x ( t n ph )) ≥ 0 , coupled conditions    t 0 = 0 , t n ph = t f , t ∈ [ t j − 1 ; t j ] .  Undisturbed human gait is usually periodic . → State x ( t f ) at the end of the step is the mirrored constellation to the state at the beginning of the step at t = 0: x (0) = ˜ x ( t f ) malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 9 / 21

Optimization , Motion generation min J ( t , x ( t ) , u ( t ) , p ) objective function x , u , p , t 0 ,..., t nph  x ( t ) = f j ( t , x ( t ) , u ( t ) , p ) , ˙ equation of motion    g j ( t , x ( t ) , u ( t ) , p ) ≥ 0 , path constraints  s.t. r ( x ( t 0 ) , x ( t 1 ) , . . . , x ( t n ph )) ≥ 0 , coupled conditions    t 0 = 0 , t n ph = t f , t ∈ [ t j − 1 ; t j ] .  Undisturbed human gait is usually periodic . → State x ( t f ) at the end of the step is the mirrored constellation to the state at the beginning of the step at t = 0: x (0) = ˜ x ( t f ) + p s . → Assumption: with push, step will remain as periodic as possible. → Include slack variables p s in objective function. malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 9 / 21

Optimization , Motion generation min J ( t , x ( t ) , u ( t ) , p ) objective function x , u , p , t 0 ,..., t nph  x ( t ) = f j ( t , x ( t ) , u ( t ) , p ) , ˙ equation of motion    g j ( t , x ( t ) , u ( t ) , p ) ≥ 0 , path constraints  s.t. r ( x ( t 0 ) , x ( t 1 ) , . . . , x ( t n ph )) ≥ 0 , coupled conditions    t 0 = 0 , t n ph = t f , t ∈ [ t j − 1 ; t j ] .  Objective function for motion generation n ph � t j s W p p s + 1 � J ( t , x ( t ) , u ( t ) , p ) = p T u ( t ) T W u u ( t ) dt . p SL t j − 1 j =1 malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 10 / 21

Solution algorithm , O ptimal Equations of N on L inear Q uadratic C ontrol- Motion P rogram Sub P roblem P roblem min J ( z ) s.t. min J ( z ) s.t. f , r x = f ( z , t ) ˙ x k +1 = ˜ min Q ( d ) ˙ x = f ( z , t ) ˜ f (˜ z k , t ) r = 0 d r = 0 ˜ r = 0 z Multiple SQP Shooting RBDL 1 MUSCOD-II 2 1 Rigid-body dynamics library by M. Felis, ORB, IWR, University of Heidelberg 2 by H. G. Bock, D. B. Leineweber, et al., SimOPT, IWR, University of Heidelberg malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 11 / 21

Motion generation , Pushes applied form the back with contact point at the pelvis. F p x ( t ) = c ( t − t p 0 ) 2 ( t − t p f ) 2 , F p c = 16 (( t p f − t p 0 ) 2 ) malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 12 / 21

Motion generation - Step Length and Periodicity , Step length increases the stronger the push. Less periodic the stronger the push. Hip and ankle joints less periodic than other joints. malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 13 / 21

Motion Generation - Right Ankle Motion and Torques , Decrease in joint angle. No significantly higher velocity for stronger pushes. Joint torques are distinctly higher for stronger pushes. R. Malin Schemschat, Debora Clever, Martin L. Felis and Katja Mombaur: Optimal Push Recovery for Periodic Walking Motions ; IFAC International Workshop on Periodic Control Systems (PSYCO2016) malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 14 / 21

Motion fitting , Optimal Control Problem min J ( t , x ( t ) , u ( t ) , p ) objective function x , u , p , t 0 ,..., t nph  x ( t ) = f j ( t , x ( t ) , u ( t ) , p ) , ˙ equation of motion    g j ( t , x ( t ) , u ( t ) , p ) ≥ 0 , path constraints  s.t.     t 0 = 0 , t n ph = t f , t ∈ [ t j − 1 ; t j ] . Objective function for motion fitting n ref q k ( t )) 2 + u ( t ) T W u u ( t ) . � φ j ( x ( t ) , u ( t ) , p ) = ( q k ( x , u , t ) − ˜ k =0 malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 15 / 21

Generation of Reference Data , Viconn MMM convert Experiments Trajectories of Kinematic Dynamic (record force marker points model model and motion) malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 16 / 21

Motion fitting , 7 motions of the same subject Pushes are applied from the back, at 3 different locations at spine: pelvis, middle and upper trunk, during swing phase of left leg. Pushes differ in strength, profile and timing One single step modelled malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 17 / 21

Motion fitting - Results , Higher internal torque results in change of joint angle velocity. Opposite does not hold because influence of the dynamics of the model that cannot be measured. R. Malin Schemschat, Debora Clever, Martin L. Felis, Enrico Chiovetto, Martin Giese, Katja Mombaur: Joint Torque Analysis of Push Recovery Motions during Human Walking ; International Conference on Biomedical Robotics and Biomechatronics (BioRob2016) malin.schemschat@iwr.uni-heidelberg.de , September 1, 2016 18 / 21