Description
This is a base class for solvers that use direct collocation to convert an optimal control problem into a generic nonlinear programming problem.
The best resource for learning about direct collocation is the Betts textbook:
Betts, John T. Practical methods for optimal control and estimation using nonlinear programming. Vol. 19. Siam, 2010.
Transcription scheme
The transcription_scheme setting allows you to choose between 'trapezoidal' and 'hermite-simpson' transcription schemes. The 'trapezoidal' option replaces the dynamics differential constraints with finite differences based on trapezoidal rule integration. The 'hermite-simpson' option uses a Hermite interpolant and Simpson integration to construct the finite differences. The 'hermite-simpson' option uses the separated Hermite-Simpson transcription approach, which allows control values at mesh interval midpoints to be free variables (see Betts textbook for more details). The setting interpolate_control_midpoints constrains control midpoint variables to be linearly interpolated from the mesh interval endpoint values (default and recommended setting). If solving problems including model kinematic constraints, the 'hermite-simpson' option is required (see Kinematic constraints section below).
Path constraints on controls with Hermite-Simpson transcription
For Hermite-Simpson transcription, the direct collocation solvers enforce the path constraints (e.g., MocoPathConstraint) at only the mesh interval endpoints (not midpoints), but control signal variables exist at both mesh interval endpoints and midpoints. Keep this in mind when using path constraints on controls (e.g., MocoControlBoundConstraint). If interpolate_control_midpoints is false, the values of a control at midpoints may differ greatly from the values at mesh interval endpoints.
Multibody dynamics mode
The multibody_dynamics_mode setting allows you to choose between expressing multibody dynamics as explicit differential equations (e.g., \( \dot{y} = f(y) \)) or implicit differential equations (e.g., \( 0 = f(y, \dot{y}) \), or inverse dynamics). Whether auxiliary dynamics (e.g., muscle fiber and activation dynamics) are implicit or explicit depends on the model component implementing those dynamics.
Kinematic constraints
All kinematic constraints included as OpenSim model constraints are supported with the 'hermite-simpson' transcription scheme setting. Kinematic constraints are automatically detected if present in the model and are converted to path constraints in the optimal control problem based on the method presented in Posa et al. 2016, 'Optimization and stabilization of trajectories for constrained dynamical systems'; see Kinematic constraints. The minimize_lagrange_multipliers and lagrange_multiplier_weight settings allow you to enable and set the weight for the minimization of all Lagrange multipliers associated with kinematic constraints in the problem. The velocity_correction_bounds setting allows you to set the bounds on the velocity correction variables that project state variables onto the constraint manifold when necessary to properly enforce defect constraints (see Posa et al. 2016 for details).
#include <Moco/Moco/MocoDirectCollocationSolver.h>
Public Member Functions | |
| OpenSim_DECLARE_PROPERTY (num_mesh_intervals, int, "The number of uniformly-sized mesh intervals for the problem " "(default: " "100). If a non-uniform mesh exists, the non-uniform mesh is used " "instead.") | |
| OpenSim_DECLARE_PROPERTY (verbosity, int, "0 for silent. 1 for only Moco's own output. " "2 for output from CasADi and the underlying solver (default: 2).") | |
| OpenSim_DECLARE_PROPERTY (transcription_scheme, std::string, "'trapezoidal' for trapezoidal transcription, or 'hermite-simpson' " "(default) for separated Hermite-Simpson transcription.") | |
| OpenSim_DECLARE_PROPERTY (interpolate_control_midpoints, bool, "If the transcription scheme is set to 'hermite-simpson', then " "enable this property to constrain the control values at mesh " "interval midpoints to be linearly interpolated from the control " "values at the mesh interval endpoints. Default: true.") | |
| OpenSim_DECLARE_PROPERTY (multibody_dynamics_mode, std::string, "Multibody dynamics are expressed as 'explicit' (default) or " "'implicit' differential equations.") | |
| OpenSim_DECLARE_PROPERTY (optim_solver, std::string, "The optimization solver to use (default: ipopt).") | |
| OpenSim_DECLARE_PROPERTY (optim_max_iterations, int, "Maximum number of iterations in the optimization solver " "(-1 for solver's default).") | |
| OpenSim_DECLARE_PROPERTY (optim_convergence_tolerance, double, "Tolerance used to determine if the objective is minimized " "(-1 for solver's default)") | |
| OpenSim_DECLARE_PROPERTY (optim_constraint_tolerance, double, "Tolerance used to determine if the constraints are satisfied " "(-1 for solver's default)") | |
| OpenSim_DECLARE_PROPERTY (optim_hessian_approximation, std::string, "When using IPOPT, 'limited-memory' (default) for quasi-Newton, or " "'exact' for full " "Newton.") | |
| OpenSim_DECLARE_PROPERTY (optim_ipopt_print_level, int, "IPOPT's verbosity (see IPOPT documentation).") | |
| OpenSim_DECLARE_OPTIONAL_PROPERTY (enforce_constraint_derivatives, bool, "'true' (default) or 'false', whether or not derivatives of " "kinematic constraints are enforced as path constraints in the " "optimal control problem.") | |
| OpenSim_DECLARE_PROPERTY (minimize_lagrange_multipliers, bool, "If enabled, a term minimizing the weighted, squared sum of " "any existing Lagrange multipliers is added to the optimal control " "problem. This may be useful for imposing uniqueness in the " "Lagrange multipliers when not enforcing model kinematic " "constraint derivatives or when the constraint Jacobian is " "singular. To set the weight for this term use the " "'lagrange_multiplier_weight' property. Default: false") | |
| OpenSim_DECLARE_PROPERTY (lagrange_multiplier_weight, double, "If the 'minimize_lagrange_multipliers' property is enabled, this " "defines the weight for the cost term added to the optimal control " "problem. Default: 1") | |
| OpenSim_DECLARE_PROPERTY (velocity_correction_bounds, MocoBounds, "For problems where model kinematic constraint derivatives are " "enforced, set the bounds on the slack variables performing the " "velocity correction to project the model coordinates back onto " "the constraint manifold. Default: [-0.1, 0.1]") | |
| OpenSim_DECLARE_PROPERTY (implicit_multibody_acceleration_bounds, MocoBounds, "Bounds on acceleration variables in implicit dynamics mode. " "Default: [-1000, 1000]") | |
| OpenSim_DECLARE_PROPERTY (implicit_auxiliary_derivative_bounds, MocoBounds, "Bounds on derivative variables for components with auxiliary " "dynamics in implicit form. Default: [-1000, 1000]") | |
| void | setMesh (const std::vector< double > &mesh) |
| Sets the mesh to a, usually non-uniform, user-defined list of mesh points to sample. More... | |
 Public Member Functions inherited from OpenSim::MocoSolver | |
| MocoSolver (const MocoProblem &problem) | |
| This calls resetProblem() with the provided problem. | |
Protected Member Functions | |
| OpenSim_DECLARE_PROPERTY (guess_file, std::string, "A MocoTrajectory file storing an initial guess.") | |
| OpenSim_DECLARE_LIST_PROPERTY (mesh, double, "Usually non-uniform, user-defined list of mesh points to sample. " "Takes precedence over uniform mesh with num_mesh_intervals.") | |
| void | constructProperties () |
Member Function Documentation
◆ setMesh()
| void OpenSim::MocoDirectCollocationSolver::setMesh | ( | const std::vector< double > & | mesh | ) |
Sets the mesh to a, usually non-uniform, user-defined list of mesh points to sample.
Takes precedence over uniform mesh with num_mesh_intervals. The user-defined mesh must start with 0, be strictly increasing (no duplicate times), and end with 1.
The documentation for this class was generated from the following file: