Learning to control from expert demonstrations
This addresses the challenge of controller design from limited data for robotics and control systems, but it is incremental as it builds on existing feedback linearization methods.
The paper tackles the problem of learning a stabilizing controller from expert demonstrations, showing that for feedback linearizable systems, a controller can be constructed with at least n+1 sufficiently long demonstrations, and extends this to a broader class of systems, demonstrated on a CrazyFlie 2.0 quadrotor.
In this paper, we revisit the problem of learning a stabilizing controller from a finite number of demonstrations by an expert. By first focusing on feedback linearizable systems, we show how to combine expert demonstrations into a stabilizing controller, provided that demonstrations are sufficiently long and there are at least $n+1$ of them, where $n$ is the number of states of the system being controlled. When we have more than $n+1$ demonstrations, we discuss how to optimally choose the best $n+1$ demonstrations to construct the stabilizing controller. We then extend these results to a class of systems that can be embedded into a higher-dimensional system containing a chain of integrators. The feasibility of the proposed algorithm is demonstrated by applying it on a CrazyFlie 2.0 quadrotor.