Solver Interfaces

Problems created with TORA.jl are first converted into an NLP problem, and then solved using Ipopt or Knitro. The two methods available for this are:

• TORA.solve_with_ipopt
• TORA.solve_with_knitro

These methods have different names but a very similar signature, purpose, and functionality.

Arguments

The main arguments of the solve_with_* methods are a Problem and a Robot. Moreover, there are optional keyword arguments that can be passed to these methods in order to customize the NLP problem transcribed from the high-level description Problem. These optional arguments are listed and explained below.

Initial Guess

initial_guess=Float64[]

This is the starting point for the solver. In other words, this is the value estimation of each decision variable. Providing a good initial guess is very important for the solver to converge quickly and in as few iterations as possible. An example of passing an initial guess is shown in Tutorial > Providing an Initial Guess.

The default value for the initial_guess is an empty array, i.e., Float64[]. During transcription, TORA.jl checks the value of initial_guess. If an array has been provided, it is passed to the solver; if a guess has not been provided, an array filled with zeros is passed to the solver instead.

Dynamics Defects

use_inv_dyn=false

TORA.jl transcribes a Problem into an NLP problem using an approach called Direct Transcription.^[1] This approach discretizes the continuous optimization problem in time, and requires nonlinear equality constraints to enforce the full dynamics of the system—known as dynamics defects. There are two options available to define these constraints: using forward dynamics or inverse dynamics. For more details, please read How TORA.jl Works.

The default value for use_inv_dyn is false. I.e., the default behaviour is to use forward dynamics. In order to use inverse dynamics for defining the dynamics defects, use_inv_dyn should be set to true.

Energy Minimization

minimise_τ=false

By default, problems formulated with TORA.jl are feasibility problems. In other words, the goal for the solver is to find a set of values that satisfies all the constraints of a Problem. However, it is possible to define a cost function to be minimized. (Or a value function to be maximized.)

The default value for minimise_τ is false. I.e., the default behaviour is to solve the feasibility problem, without optimizing any objective function. Alternatively, if minimise_τ is set to true, TORA.jl will minimize the joint torques required by the trajectory being computed.

Solver User Options

user_options=Dict()

This parameter allows to pass custom options to the actual NLP solvers, i.e., to Ipopt and to Knitro. The options that can be set depend on each solver. The list of available options for Ipopt is given here, and for Knitro here.

The default value for user_options is an empty dictionary. A dictionary of key-value pairs can be passed to the solver instead.

As an example, suppose we want to use the linear solver MA57. Then, for Ipopt we would set

user_options=Dict("linear_solver" => "ma57")  # for Ipopt

and for Knitro

user_options=Dict(KNITRO.KN_PARAM_LINSOLVER => KNITRO.KN_LINSOLVER_MA57)   # for Knitro

Methods

solve_with_ipopt(problem, robot;
                 initial_guess=Float64[],
                 use_inv_dyn=false,
                 minimise_τ=false,
                 user_options=Dict())

solve_with_knitro(problem, robot;
                  initial_guess=Float64[],
                  use_inv_dyn=false,
                  minimise_τ=false,
                  user_options=Dict())