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NamedTrajectories.jl

An elegant way to handle messy trajectory data

Notice

This package is under active development and issues may arise – please be patient and report any issues you find!

Motivation

NamedTrajectories.jl is designed to aid in the messy indexing involved in solving trajectory optimization problems of the form

\[\begin{align*} \underset{u^1_{1:T}, \dots, u^{n_c}_{1:T}}{\underset{x^1_{1:T}, \cdots, x^{n_s}_{1:T}}{\operatorname{minimize}}} &\quad J\qty(x^{1:n_s}_{1:T},u^{1:n_c}_{1:T}) \\ \text{subject to} & \quad f\qty(x^{1:n_s}_{1:T},u^{1:n_c}_{1:T}) = 0 \\ & \quad x^i_1 = x^i_{\text{initial}} \\ & \quad x^i_T = x^i_{\text{final}} \\ & \quad u^i_1 = u^i_{\text{initial}} \\ & \quad u^i_T = u^i_{\text{final}} \\ & \quad x^i_{\min} < x^i_t < x^i_{\max} \\ & \quad u^i_{\min} < u^i_t < u^i_{\max} \\ \end{align*}\]

Where $x^i_t$ is the $i$th state variable and $u^i_t$ is the $i$th control variable at timestep $t$; state and control variables can be of arbitrary dimension. The function $f$ is a nonlinear constraint function and $J$ is the objective function. These problems can have an arbitrary number of state ($n_s$) and control ($n_c$) variables, and the number of timesteps $T$ can vary as well.

In trajectory optimization problems it is common practice to bundle all of the state and control variables together into a single knot point

\[z_t = \mqty( x^1_t \\ \vdots \\ x^{n_s}_t \\ u^1_t \\ \vdots \\ u^{n_c}_t ).\]

The trajectory optimization problem can then be succinctly written as

\[\begin{align*} \underset{z_{1:T}}{\operatorname{minimize}} &\quad J\qty(z_{1:T}) \\ \text{subject to} & \quad f\qty(z_{1:T}) = 0 \\ & \quad z_1 = z_{\text{initial}} \\ & \quad z_T = z_{\text{final}} \\ & \quad z_{\min} < z_t < z_{\max} \\ \end{align*}\]

The NamedTrajectories package provides a NamedTrajectory type which abstracts away the messy indexing and vectorization details required for interfacing with numerical solvers. It also provides a variety of helpful methods for common tasks. For example, you can access the data by name or index. In the case of an index, a KnotPoint is returned which contains the data for that timestep.

Features

  • Abstract away messy indexing and vectorization details required for interfacing with numerical solvers.
  • Easily handle multiple trajectories with different names, e.g. various states and controls.
  • Simple plotting of trajectories.
  • Provide a variety of helpful methods for common tasks.

Index