Documentation  | Build Status  | License | Support |
NamedTrajectories.jl
NamedTrajectories.jl is a package for working with trajectories of named variables. It is designed to be used with the Piccolo.jl ecosystem.
Installation
NamedTrajectories.jl is registered! Install in the REPL by entering pkg mode with ] and then running
pkg> add NamedTrajectoriesor to install the latest master branch run
pkg> add NamedTrajectories#mainFeatures
- 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.
Basic Usage
Users can define NamedTrajectory types which have lots of useful functionality. 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.
using NamedTrajectories
# define number of timesteps and timestep
T = 10
dt = 0.1
# build named tuple of components and data matrices
components = (
x = rand(3, T),
u = rand(2, T),
)
# build trajectory
traj = NamedTrajectory(components; timestep=dt, controls=:u)
# access data by name
traj.x # returns 3x10 matrix of x data
traj.u # returns 2x10 matrix of u data
z1 = traj[1] # returns KnotPoint with x and u data
z1.x # returns 3 element vector of x data at timestep 1
z1.u # returns 2 element vector of u data at timestep 1
traj.data # returns data as 5x10 matrix
traj.names # returns names as tuple (:x, :u)Motivation
NamedTrajectories.jl is designed to aid in the messy indexing involved in solving trajectory optimization problems of the form
\[\begin{aligned} \arg \min_{\mathbf{Z}}\quad & J(\mathbf{Z}) \\ \nonumber \text{s.t.}\qquad & \mathbf{f}(\mathbf{Z}) = 0 \\ \nonumber & \mathbf{g}(\mathbf{Z}) \le 0 \end{aligned}\]
where $\mathbf{Z}$ is a trajectory.
In more detail, this problem might look something like
\[\begin{align*} \underset{u^1_{1:T}, \dots, u^{n_c}_{1:T}}{\underset{x^1_{1:T}, \cdots, x^{n_s}_{1:T}}{\operatorname{minimize}}} &\quad J\qty(x^{1:n_s}_{1:T},u^{1:n_c}_{1:T}) \\ \text{subject to} & \quad f\qty(x^{1:n_s}_{1:T},u^{1:n_c}_{1:T}) = 0 \\ & \quad x^i_1 = x^i_{\text{initial}} \\ & \quad x^i_T = x^i_{\text{final}} \\ & \quad u^i_1 = u^i_{\text{initial}} \\ & \quad u^i_T = u^i_{\text{final}} \\ & \quad x^i_{\min} < x^i_t < x^i_{\max} \\ & \quad u^i_{\min} < u^i_t < u^i_{\max} \\ \end{align*}\]
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.
It is common practice in trajectory optimization 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.