Tracking control is a technique which is similar to PID control and has the aim to implement a robust feedback loop for generating action-signals. In contrast to a line following robot, tracking control is oriented in a time-action space. On the x-axis the timecode is presented, for example 0 seconds, 0.5 seconds and 1 seconds, while on the y-axis the value of the signal is plotted. The value can be the position of a robot, the angle of an inverted pendulum or the x-position of an object. Even in simple problems like the inverted pendulum, the number of parameters on the y-axis is greater than 1. The spline of all parameters of the time are equal to a movement pattern.
The problem is how to summarize the different values to a single signal. This is needed for determine the similarity in a “Learning from demonstration” experiment. The human-operator is doing an action, and the aim of the robot is to reproduce the movement pattern. I've searched a bit the topic in Google Scholar and found a paper: A humanoid robot standing up through learning from demonstration using a multimodal reward function but I'm a bit unsure, because there is so much math and it is also dedicated to ZMP biped walking. What I'm searching is more a general idea of how to compress different splines into one reward function.
Description of the bug
Tracking a single spline which is plotted in a diagram is easy. The difference between the current value and the desired value is measured and the feedback-controller reduces the difference. If the number of splines is 2 this concept fails. For example, spline #1 represents the angle and spline #2 the velocity over time. The current state has 2 variables and the desired state has 2 variables. How can I program a steering-controller for a multi-spline?