Optimal Control Problems#

Optimal control problem formulation and solution methods for biosym.

Constraint Functions#

Constraint functions for optimal control problems in biosym.

This module provides constraint handling for optimal control problems, including constraint evaluation, Jacobian computation, and integration with collocation methods for biomechanical motion optimization.

class biosym.ocp.confun.Constraints(model, settings)#

Bases: object

Handle constraints for optimal control problems.

This class manages constraint evaluation, Jacobian computation, and constraint structure analysis for biomechanical optimal control problems. It integrates various constraint types including dynamics, periodicity, discretization, and custom user constraints.

model#

The biomechanical model containing system dynamics

Type:

BiosymModel

settings#

Configuration settings for constraint handling

Type:

dict

constraint_list#

List of active constraint objects

Type:

list

ncon#

Total number of constraint equations

Type:

int

add_constraint(name, weight, args=None)#

Add a constraint to the optimal control problem.

Parameters:

  • name (str or class) – Either a string name of a constraint class or a constraint class object. If string, the class will be looked up in the global namespace.

  • weight (float, int, or str) – Weighting factor for the constraint in the optimization. Can be numeric value or special string like “1/BW” for bodyweight normalization.

  • args (dict, optional) – Additional arguments to pass to the constraint constructor.

Raises:

ValueError – If the constraint class name is not found or invalid constraint object provided.

Notes

  • Constraints are instantiated with the model and settings objects

  • Weights are stored for later use in constraint evaluation

  • Constraint information (number of constraints, Jacobian sparsity) is recorded

biosym.ocp.confun.evaluate_constraints(constraint_functions, weights, ncon, c_start, states_list, globals_dict=None)#

Evaluate all constraints for the current state of the optimal control problem.

This function efficiently evaluates all constraint functions and assembles them into a single constraint vector with appropriate weighting. It’s designed to be JIT-compiled for performance during optimization.

Parameters:

  • constraint_functions (list) – List of constraint functions to evaluate.

  • weights (list) – Weighting factors for each constraint type.

  • ncon (int) – Total number of constraints.

  • c_start (list) – Starting indices for each constraint type in the output vector.

  • states_list (dict) – Dictionary containing current state variables (positions, velocities, etc.).

  • globals_dict (dict, optional) – Dictionary containing global variables or parameters.

Returns:

Constraint vector of shape (ncon,) containing all weighted constraint values.

Return type:

jnp.ndarray

Notes

  • This function is typically JIT-compiled for optimal performance

  • Constraints are weighted and concatenated into a single vector

  • Used during optimization iterations to evaluate constraint violations

biosym.ocp.confun.evaluate_jacobian(jacobian_functions, weights, nnz, c_start, nnz_start, states_list, globals_dict=None)#

Evaluate the Jacobian matrix of all constraints for gradient-based optimization.

This function computes the sparse Jacobian matrix of all constraints with respect to the state variables. The Jacobian is essential for efficient gradient-based optimization algorithms used in optimal control.

Parameters:

  • jacobian_functions (list) – List of Jacobian functions for each constraint type.

  • weights (list) – Weighting factors for each constraint type.

  • nnz (int) – Total number of non-zero entries in the sparse Jacobian.

  • c_start (list) – Starting row indices for each constraint type in the Jacobian.

  • nnz_start (list) – Starting indices for non-zero entries of each constraint type.

  • states_list (dict) – Dictionary containing current state variables.

  • globals_dict (dict, optional) – Dictionary containing global variables or parameters.

Returns:

Sparse Jacobian matrix in COO format as (rows, cols, data) where: - rows: Row indices of non-zero entries - cols: Column indices of non-zero entries - data: Values of non-zero entries (weighted)

Return type:

tuple of jnp.ndarray

Notes

  • Returns sparse matrix in COO (coordinate) format for efficiency

  • Jacobian entries are weighted according to constraint weights

  • Row indices are adjusted to account for constraint concatenation

  • Used by optimization algorithms for computing search directions

Objective Functions#

Collocation Methods#

OCP Utilities#