Solvers

mutable struct iLQRSolverOptions{T} <: TrajectoryOptimization.AbstractSolverOptions{T}

Solver options for the iterative LQR (iLQR) solver.

• verbose

  Print summary at each iteration. Default: false

• live_plotting

  Live plotting. Default: :off

• cost_tolerance

  dJ < ϵ, cost convergence criteria for unconstrained solve or to enter outerloop for constrained solve. Default: 0.0001

• gradient_type

  gradient type: :todorov, :feedforward. Default: :todorov

• gradient_norm_tolerance

  gradient_norm < ϵ, gradient norm convergence criteria. Default: 1.0e-5

• iterations

  iLQR iterations. Default: 300

• dJ_counter_limit

  restricts the total number of times a forward pass fails, resulting in regularization, before exiting. Default: 10

• square_root

  use square root method backward pass for numerical conditioning. Default: false

• line_search_lower_bound

  forward pass approximate line search lower bound, 0 < linesearchlowerbound < linesearchupperbound. Default: 1.0e-8

• line_search_upper_bound

  forward pass approximate line search upper bound, 0 < linesearchlowerbound < linesearchupperbound < ∞. Default: 10.0

• iterations_linesearch

  maximum number of backtracking steps during forward pass line search. Default: 20

• bp_reg_initial

  initial regularization. Default: 0.0

• bp_reg_increase_factor

  regularization scaling factor. Default: 1.6

• bp_reg_max

  maximum regularization value. Default: 1.0e8

• bp_reg_min

  minimum regularization value. Default: 1.0e-8

• bp_reg_type

  type of regularization- control: () + ρI, state: (S + ρI); see Synthesis and Stabilization of Complex Behaviors through Online Trajectory Optimization. Default: :control

• bp_reg_fp

  additive regularization when forward pass reaches max iterations. Default: 10.0

• bp_sqrt_inv_type

  type of matrix inversion for bp sqrt step. Default: :pseudo

• bp_reg_sqrt_initial

  initial regularization for square root method. Default: 1.0e-6

• bp_reg_sqrt_increase_factor

  regularization scaling factor for square root method. Default: 10.0

• bp_reg

  Default: false

• max_cost_value

  maximum cost value, if exceded solve will error. Default: 1.0e8

• max_state_value

  maximum state value, evaluated during rollout, if exceded solve will error. Default: 1.0e8

• max_control_value

  maximum control value, evaluated during rollout, if exceded solve will error. Default: 1.0e8

• static_bp

  Default: true

• log_level

  Default: InnerLoop

struct AugmentedLagrangianSolver <: TrajectoryOptimization.AbstractSolver{T}

Augmented Lagrangian (AL) is a standard tool for constrained optimization. For a trajectory optimization problem of the form:

AL methods form the following augmented Lagrangian function:

This function is then minimized with respect to the primal variables using any unconstrained minimization solver (e.g. iLQR). After a local minima is found, the AL method updates the Lagrange multipliers λ and the penalty terms μ and repeats the unconstrained minimization. AL methods have superlinear convergence as long as the penalty term μ is updated each iteration.

mutable struct AugmentedLagrangianSolverOptions{T} <: TrajectoryOptimization.AbstractSolverOptions{T}

Solver options for the augmented Lagrangian solver.

• verbose

  Print summary at each iteration. Default: false

• opts_uncon

  unconstrained solver options. Default: UnconstrainedSolverOptions{Float64}()

• cost_tolerance

  dJ < ϵ, cost convergence criteria for unconstrained solve or to enter outerloop for constrained solve. Default: 0.0001

• cost_tolerance_intermediate

  dJ < ϵ_int, intermediate cost convergence criteria to enter outerloop of constrained solve. Default: 0.001

• gradient_norm_tolerance

  gradient_norm < ϵ, gradient norm convergence criteria. Default: 1.0e-5

• gradient_norm_tolerance_intermediate

  gradientnormint < ϵ, gradient norm intermediate convergence criteria. Default: 1.0e-5

• constraint_tolerance

  max(constraint) < ϵ, constraint convergence criteria. Default: 0.001

• constraint_tolerance_intermediate

  max(constraint) < ϵ_int, intermediate constraint convergence criteria. Default: 0.001

• iterations

  maximum outerloop updates. Default: 30

• dual_max

  global maximum Lagrange multiplier. If NaN, use value from constraint Default: NaN

• penalty_max

  global maximum penalty term. If NaN, use value from constraint Default: NaN

• penalty_initial

  global initial penalty term. If NaN, use value from constraint Default: NaN

• penalty_scaling

  global penalty update multiplier; penalty_scaling > 1. If NaN, use value from constraint Default: NaN

• penalty_scaling_no

  penalty update multiplier when μ should not be update, typically 1.0 (or 1.0 + ϵ). Default: 1.0

• constraint_decrease_ratio

  ratio of current constraint to previous constraint violation; 0 < constraintdecreaseratio < 1. Default: 0.25

• outer_loop_update_type

  type of outer loop update (default, feedback). Default: :default

• active_constraint_tolerance

  numerical tolerance for constraint violation. Default: 0.0

• kickout_max_penalty

  terminal solve when maximum penalty is reached. Default: false

• reset_duals

  Default: true

• reset_penalties

  Default: true

• log_level

  Default: OuterLoop

struct ALTROSolver{T, S} <: ConstrainedSolver{T}

Augmented Lagrangian Trajectory Optimizer (ALTRO) is a solver developed by the Robotic Exploration Lab at Stanford University. The solver is special-cased to solve Markov Decision Processes by leveraging the internal problem structure.

ALTRO consists of two "phases":

1. AL-iLQR: iLQR is used with an Augmented Lagrangian framework to solve the problem quickly to rough constraint satisfaction
2. Projected Newton: A collocation-flavored active-set solver projects the solution from AL-iLQR onto the feasible subspace to achieve machine-precision constraint satisfaction.

mutable struct ALTROSolverOptions{T} <: TrajectoryOptimization.AbstractSolverOptions{T}

Solver options for the ALTRO solver.

• verbose

  Default: false

• opts_al

  Augmented Lagrangian solver options. Default: AugmentedLagrangianSolverOptions{Float64}()

• constraint_tolerance

  constraint tolerance Default: 1.0e-5

• infeasible

  Use infeasible model (augment controls to make it fully actuated) Default: false

• dynamically_feasible_projection

  project infeasible results to feasible space using TVLQR. Default: true

• resolve_feasible_problem

  resolve feasible problem after infeasible solve. Default: true

• penalty_initial_infeasible

  initial penalty term for infeasible controls. Default: 1.0

• penalty_scaling_infeasible

  penalty update rate for infeasible controls. Default: 10.0

• projected_newton

  finish with a projecte newton solve. Default: true

• opts_pn

  options for projected newton solver. Default: ProjectedNewtonSolverOptions{Float64}()

• projected_newton_tolerance

  constraint satisfaction tolerance that triggers the projected newton solver. If set to a non-positive number it will kick out when the maximum penalty is reached. Default: 0.001

struct DIRCOLSolver{Q<:QuadratureRule, L, T, N, M, NM} <: DirectSolver{T}

Direct Collocation Solver. Uses a commerical NLP solver to solve the Trajectory Optimization problem. Uses the MathOptInterface to interface with the NLP.

mutable struct DIRCOLSolverOptions{T} <: TrajectoryOptimization.DirectSolverOptions{T}

Solver options for the Direct Collocation solver. Most options are passed to the NLP through the opts dictionary

• nlp

  NLP Solver to use. See MathOptInterface for available NLP solvers Default: Ipopt.Optimizer()

• opts

  Options dictionary for the nlp solver Default: Dict{Symbol, Any}()

• verbose

  Print output to console Default: true

• constraint_tolerance

  Feasibility tolerance Default: -1.0

struct ProjectedNewtonSolver{T, N, M, NM} <: DirectSolver{T}

Projected Newton Solver Direct method developed by the REx Lab at Stanford University Achieves machine-level constraint satisfaction by projecting onto the feasible subspace. It can also take a full Newton step by solving the KKT system. This solver is to be used exlusively for solutions that are close to the optimal solution. It is intended to be used as a "solution polishing" method for augmented Lagrangian methods.

mutable struct ProjectedNewtonSolverOptions{T} <: TrajectoryOptimization.DirectSolverOptions{T}

Solver options for the Projected Newton solver.

• verbose

  Default: true

• n_steps

  Default: 2

• solve_type

  Default: :feasible

• active_set_tolerance

  Default: 0.001

• constraint_tolerance

  Default: 1.0e-6

• ρ

  Default: 0.01

• r_threshold

  Default: 1.1