  Imitation learning is a paradigm to address complex motion planning problems
by learning a policy to imitate an expert's behavior. However, relying solely
on the expert's data might lead to unsafe actions when the robot deviates from
the demonstrated trajectories. Stability guarantees have previously been
provided utilizing nonlinear dynamical systems, acting as high-level motion
planners, in conjunction with the Lyapunov stability theorem. Yet, these
methods are prone to inaccurate policies, high computational cost, sample
inefficiency, or quasi stability when replicating complex and highly nonlinear
trajectories. To mitigate this problem, we present an approach for learning a
globally stable nonlinear dynamical system as a motion planning policy. We
model the nonlinear dynamical system as a parametric polynomial and learn the
polynomial's coefficients jointly with a Lyapunov candidate. To showcase its
success, we compare our method against the state of the art in simulation and
conduct real-world experiments with the Kinova Gen3 Lite manipulator arm. Our
experiments demonstrate the sample efficiency and reproduction accuracy of our
method for various expert trajectories, while remaining stable in the face of
perturbations.
