Dynamical System

The Dynamical System panel allows to test, tweak and observe how different algorithms model a dynamical system in a N-dimensional space: "the canvas".
The DS implemented in MLDemos are time-independent and provide, for each position in space, a desired velocity.

Trajectories are drawn by hand (or imported) as positions in space. A velocity for each step will be computed uniformly using the user-defined dT temporal step.

The canvas will display the results of the dynamical system in multiple layers, which can be toggled using the display options. These are: For multi-dimensional data, it is not possible to display the dynamical system flow in space, therefore only the reconstruction of the known trajectories is provided.

Moving the mouse on the canvas will display the computed trajectory from the starting position until the dynamical system stops or deviates to infinity.
The canvas can also animate learned trajectories from given positions defined by the Drag Me target button.

Obstacle Avoidance
The Dynamical System can be coupled to an obstacle avoidance method, which will adapt the dynamical system so as not to penetrate obstacles put in the canvas. New obstacles can be added to the canvas using the Obstacle tool in the drawing options.

In Practice
The easiest way to test the dynamical system is to:
  1. Draw some trajectories (left-click and drag around) in the canvas
  2. Click on "Train"
This should train the dynamical system and draw the result.

Options and Commands
The interface for dynamical system (the right-hand side of the Algorithm Options dialog) provides the following commands: The comparison is performed by computing the step-by-step error for the known trajectories, or the error between ending points,
to evaluate the DS stability at target.

The following options are available: All other options are algorithm-dependent and should be described in the help menu of the algorithm itself.