On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics

TL;DR

The paper addresses planning and control for underactuated robots with uncertain dynamics by introducing an iterative framework that alternates offline optimization-based planning with online partial feedback linearization (PFL) control. Central to the method is learning perturbations to active and passive subsystems via Gaussian Process regressors, yielding two corrections $\boldsymbol{\varepsilon}_{a}$ and $\boldsymbol{\varepsilon}_{p}$ that feedback into planning and control respectively. The approach enables dynamically feasible trajectory generation and accurate tracking even under large model mismatches, demonstrated on the Pendubot through simulations and real experiments, where convergence occurs after only a few iterations. Notably, the method does not require torque sensing and can incorporate state/input constraints, suggesting strong practical applicability to a range of underactuated systems and maneuvers.

Abstract

We present an iterative approach for planning and controlling motions of underactuated robots with uncertain dynamics. At its core, there is a learning process which estimates the perturbations induced by the model uncertainty on the active and passive degrees of freedom. The generic iteration of the algorithm makes use of the learned data in both the planning phase, which is based on optimization, and the control phase, where partial feedback linearization of the active dofs is performed on the model updated on-line. The performance of the proposed approach is shown by comparative simulations and experiments on a Pendubot executing various types of swing-up maneuvers. Very few iterations are typically needed to generate dynamically feasible trajectories and the tracking control that guarantees their accurate execution, even in the presence of large model uncertainties.

Figures (8)

• Figure 1: The Pendubot performing two different swing-up maneuvers using the proposed method: the targets are the up-up equilibrium (first row) and the down-up equilibrium (second row). See the accompanying video.
• Figure 2: Block diagram of the generic iteration of the proposed algorithm. Solid signal lines represent data that are used at each time step, whereas dashed lines are data transferred at the end of the iteration.
• Figure 3: The Pendubot and its generalized coordinates.
• Figure 4: Simulation scenario 1 ( swing-up to${\boldsymbol{q}}^{\,\text{u-u}}$): results without learning. Left: Using the nominal model for planning and the true model for control. Right: Vice versa.
• Figure 7: Simulation scenario 2 (transfer between unstable equilibria): results with the proposed approach. Two iterations are needed to achieve convergence.