This example conducts a 2-D prediction of walking, employing a MocoPerodicityGoal.
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%
OpenSim Moco: example2DWalking.m %
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% Copyright (c) 2019 Stanford University and the Authors %
% %
% Author(s): Brian Umberger %
% %
% Licensed under the Apache License, Version 2.0 (the "License"); you may %
% not use this file except in compliance with the License. You may obtain a %
% copy of the License at http:
% %
% Unless required by applicable law or agreed to in writing, software %
% distributed under the License is distributed on an "AS IS" BASIS, %
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %
% See the License for the specific language governing permissions and %
% limitations under the License. %
% -------------------------------------------------------------------------- %
% This is a Matlab implementation of an example optimal control
% problem (2-D walking) orginally created in C++ by Antoine Falisse
% (see: example2DWalking.cpp).
%
% This example features two different optimal control problems:
% - The first problem is a tracking simulation of walking.
% - The second problem is a predictive simulation of walking.
%
% The code is inspired from Falisse A, Serrancoli G, Dembia C, Gillis J,
% De Groote F: Algorithmic differentiation improves the computational
% efficiency of OpenSim-based trajectory optimization of human movement.
% PLOS One, 2019.
%
% Model
% -----
% The model described in the file '2D_gait.osim' included in this file is a
% modified version of the 'gait10dof18musc.osim' available within OpenSim. We
% replaced the moving knee flexion axis by a fixed flexion axis, replaced the
% Millard2012EquilibriumMuscles by DeGrooteFregly2016Muscles, and added
% SmoothSphereHalfSpaceForces (two contacts per foot) to model the
% contact interactions between the feet and the ground.
%
% Do not use this model for research. The path of the gastroc muscle contains
% an error--the path does not cross the knee joint.
%
% Data
% ----
% The coordinate data included in the 'referenceCoordinates.sto' comes from
% predictive simulations generated in Falisse et al. 2019. As such,
% they deviate slightly from typical experimental gait data.
clear;
% Load the Moco libraries
import org.opensim.modeling.*;
% ---------------------------------------------------------------------------
% Set up a coordinate tracking problem where the goal is to minimize the
% difference between provided and simulated coordinate values and speeds (and
% ground reaction forces), as well as to minimize an effort cost (squared
% controls). The provided data represents half a gait cycle. Endpoint
% constraints enforce periodicity of the coordinate values (except for
% pelvis tx) and speeds, coordinate actuator controls, and muscle activations.
% Define the optimal control problem
% ==================================
track = MocoTrack();
track.setName('gaitTracking');
% Set the weights for the terms in the objective function. The values below were
% obtained by trial and error.
%
% Note: If GRFTrackingWeight is set to 0 then GRFs will not be tracked. Setting
% GRFTrackingWeight to 1 will cause the total tracking error (states + GRF) to
% have about the same magnitude as control effort in the final objective value.
controlEffortWeight = 10;
stateTrackingWeight = 1;
GRFTrackingWeight = 1;
% Reference data for tracking problem
tableProcessor = TableProcessor('referenceCoordinates.sto');
tableProcessor.append(TabOpLowPassFilter(6));
modelProcessor = ModelProcessor('2D_gait.osim');
track.setModel(modelProcessor);
track.setStatesReference(tableProcessor);
track.set_states_global_tracking_weight(stateTrackingWeight);
track.set_allow_unused_references(true);
track.set_track_reference_position_derivatives(true);
track.set_apply_tracked_states_to_guess(true);
track.set_initial_time(0.0);
track.set_final_time(0.47008941);
study = track.initialize();
problem = study.updProblem();
% Goals
% =====
% Symmetry
% --------
% This goal allows us to
simulate only one step with left-right symmetry
% that we can then double to create a full gait cycle.
symmetryGoal = MocoPeriodicityGoal('symmetryGoal');
problem.addGoal(symmetryGoal);
model = modelProcessor.process();
model.initSystem();
% Symmetric coordinate values (except for pelvis_tx) and speeds. Here, we
% constrain final coordinate values of one leg to match the initial value of the
% other leg. Or, in the case of the pelvis_tx value, we constrain the final
% value to be the same as the initial value.
for i = 1:model.getNumStateVariables()
currentStateName = string(model.getStateVariableNames().getitem(i-1));
if startsWith(currentStateName , '/jointset')
if contains(currentStateName,'_r')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_r','_l'));
symmetryGoal.addStatePair(pair);
end
if contains(currentStateName,'_l')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_l','_r'));
symmetryGoal.addStatePair(pair);
end
if (~contains(currentStateName,'_r') && ...
~contains(currentStateName,'_l') && ...
~contains(currentStateName,'pelvis_tx/value') && ...
~contains(currentStateName,'/activation'))
symmetryGoal.addStatePair(MocoPeriodicityGoalPair(currentStateName));
end
end
end
% Symmetric muscle activations. Here, we constrain final muscle activation
% values of one leg to match the initial activation values of the other leg.
for i = 1:model.getNumStateVariables()
currentStateName = string(model.getStateVariableNames().getitem(i-1));
if endsWith(currentStateName,'/activation')
if contains(currentStateName,'_r')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_r','_l'));
symmetryGoal.addStatePair(pair);
end
if contains(currentStateName,'_l')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_l','_r'));
symmetryGoal.addStatePair(pair);
end
end
end
% The lumbar coordinate actuator control is symmetric.
symmetryGoal.addControlPair(MocoPeriodicityGoalPair('/lumbarAct'));
% Get a reference to the MocoControlGoal that is added to every MocoTrack
% problem by default and change the weight
effort = MocoControlGoal.safeDownCast(problem.updGoal('control_effort'));
effort.setWeight(controlEffortWeight);
% Optionally, add a contact tracking goal.
if GRFTrackingWeight ~= 0
% Track the right and left vertical and fore-aft ground reaction forces.
contactTracking = MocoContactTrackingGoal('contact', GRFTrackingWeight);
contactTracking.setExternalLoadsFile('referenceGRF.xml');
forceNamesRightFoot = StdVectorString();
forceNamesRightFoot.add('contactHeel_r');
forceNamesRightFoot.add('contactFront_r');
contactTracking.addContactGroup(forceNamesRightFoot, 'Right_GRF');
forceNamesLeftFoot = StdVectorString();
forceNamesLeftFoot.add('contactHeel_l');
forceNamesLeftFoot.add('contactFront_l');
contactTracking.addContactGroup(forceNamesLeftFoot, 'Left_GRF');
contactTracking.setProjection('plane');
contactTracking.setProjectionVector(Vec3(0, 0, 1));
problem.addGoal(contactTracking);
end
% Bounds
% ======
problem.setStateInfo('/jointset/groundPelvis/pelvis_tilt/value', [-20*pi/180, -10*pi/180]);
problem.setStateInfo('/jointset/groundPelvis/pelvis_tx/value', [0, 1]);
problem.setStateInfo('/jointset/groundPelvis/pelvis_ty/value', [0.75, 1.25]);
problem.setStateInfo('/jointset/hip_l/hip_flexion_l/value', [-10*pi/180, 60*pi/180]);
problem.setStateInfo('/jointset/hip_r/hip_flexion_r/value', [-10*pi/180, 60*pi/180]);
problem.setStateInfo('/jointset/knee_l/knee_angle_l/value', [-50*pi/180, 0]);
problem.setStateInfo('/jointset/knee_r/knee_angle_r/value', [-50*pi/180, 0]);
problem.setStateInfo('/jointset/ankle_l/ankle_angle_l/value', [-15*pi/180, 25*pi/180]);
problem.setStateInfo('/jointset/ankle_r/ankle_angle_r/value', [-15*pi/180, 25*pi/180]);
problem.setStateInfo('/jointset/lumbar/lumbar/value', [0, 20*pi/180]);
% Solve the problem
% =================
gaitTrackingSolution = study.solve();
% Create a full stride from the periodic single step solution.
fullStride.write('gaitTracking_solution_fullStride.sto');
% Uncomment next line to visualize the result
% study.visualize(fullStride);
% Extract ground reaction forces
% ==============================
contact_r = StdVectorString();
contact_l = StdVectorString();
contact_r.add('contactHeel_r');
contact_r.add('contactFront_r');
contact_l.add('contactHeel_l');
contact_l.add('contactFront_l');
fullStride,contact_r,contact_l);
STOFileAdapter.write(externalForcesTableFlat, ...
'gaitTracking_solutionGRF_fullStride.sto');
% Uncomment next line to terminate after solving only the tracking problem
% return;
%------------------------------------------------------------------------
% Set up a gait prediction problem where the goal is to minimize effort
% (squared controls) divided by distance traveled while enforcing symmetry of
% the walking cycle and a prescribed average gait speed through endpoint
% constraints. The solution of the coordinate tracking problem is
% used as an initial guess for the prediction.
% Define the optimal control problem
% ==================================
study = MocoStudy();
study.setName('gaitPrediction');
problem = study.updProblem();
modelProcessor = ModelProcessor('2D_gait.osim');
problem.setModelProcessor(modelProcessor);
% Goals
% =====
% Symmetry (to permit simulating only one step)
symmetryGoal = MocoPeriodicityGoal('symmetryGoal');
problem.addGoal(symmetryGoal);
model = modelProcessor.process();
model.initSystem();
% Symmetric coordinate values (except for pelvis_tx) and speeds
for i = 1:model.getNumStateVariables()
currentStateName = string(model.getStateVariableNames().getitem(i-1));
if startsWith(currentStateName , '/jointset')
if contains(currentStateName,'_r')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_r','_l') );
symmetryGoal.addStatePair(pair);
end
if contains(currentStateName,'_l')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_l','_r'));
symmetryGoal.addStatePair(pair);
end
if (~contains(currentStateName,'_r') && ...
~contains(currentStateName,'_l') && ...
~contains(currentStateName,'pelvis_tx/value') && ...
~contains(currentStateName,'/activation'))
symmetryGoal.addStatePair(MocoPeriodicityGoalPair(currentStateName));
end
end
end
% Symmetric muscle activations
for i = 1:model.getNumStateVariables()
currentStateName = string(model.getStateVariableNames().getitem(i-1));
if endsWith(currentStateName,'/activation')
if contains(currentStateName,'_r')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_r','_l'));
symmetryGoal.addStatePair(pair);
end
if contains(currentStateName,'_l')
pair = MocoPeriodicityGoalPair(currentStateName, ...
regexprep(currentStateName,'_l','_r'));
symmetryGoal.addStatePair(pair);
end
end
end
% Symmetric coordinate actuator controls
symmetryGoal.addControlPair(MocoPeriodicityGoalPair('/lumbarAct'));
% Prescribed average gait speed
speedGoal = MocoAverageSpeedGoal('speed');
problem.addGoal(speedGoal);
speedGoal.set_desired_average_speed(1.2);
% Effort over distance
effortGoal = MocoControlGoal('effort', 10);
problem.addGoal(effortGoal);
effortGoal.setExponent(3);
effortGoal.setDivideByDisplacement(true);
% Bounds
% ======
problem.setTimeBounds(0, [0.4, 0.6]);
problem.setStateInfo('/jointset/groundPelvis/pelvis_tilt/value', [-20*pi/180, -10*pi/180]);
problem.setStateInfo('/jointset/groundPelvis/pelvis_tx/value', [0, 1]);
problem.setStateInfo('/jointset/groundPelvis/pelvis_ty/value', [0.75, 1.25]);
problem.setStateInfo('/jointset/hip_l/hip_flexion_l/value', [-10*pi/180, 60*pi/180]);
problem.setStateInfo('/jointset/hip_r/hip_flexion_r/value', [-10*pi/180, 60*pi/180]);
problem.setStateInfo('/jointset/knee_l/knee_angle_l/value', [-50*pi/180, 0]);
problem.setStateInfo('/jointset/knee_r/knee_angle_r/value', [-50*pi/180, 0]);
problem.setStateInfo('/jointset/ankle_l/ankle_angle_l/value', [-15*pi/180, 25*pi/180]);
problem.setStateInfo('/jointset/ankle_r/ankle_angle_r/value', [-15*pi/180, 25*pi/180]);
problem.setStateInfo('/jointset/lumbar/lumbar/value', [0, 20*pi/180]);
% Configure the solver
% ====================
solver = study.initCasADiSolver();
solver.set_num_mesh_intervals(50);
solver.set_verbosity(2);
solver.set_optim_solver('ipopt');
solver.set_optim_convergence_tolerance(1e-4);
solver.set_optim_constraint_tolerance(1e-4);
solver.set_optim_max_iterations(1000);
solver.setGuess(gaitTrackingSolution); % Use tracking solution as initial guess
% Solve problem
% =============
gaitPredictionSolution = study.solve();
% Create a full stride from the periodic single step solution.
fullStride.write('gaitPrediction_solution_fullStride.sto');
% Visualize the result.
study.visualize(fullStride);
% Extract ground reaction forces
% ==============================
contact_r = StdVectorString();
contact_l = StdVectorString();
contact_r.add('contactHeel_r');
contact_r.add('contactFront_r');
contact_l.add('contactHeel_l');
contact_l.add('contactFront_l');
% Create a conventional ground reaction forces file by summing the contact
% forces of contact spheres on each foot.
% For details, view the Doxygen documentation for
fullStride, contact_r, contact_l);
STOFileAdapter.write(externalForcesTableFlat, ...
'gaitPrediction_solutionGRF_fullStride.sto');
1.8.14