Active task design in adaptive control of redundant robotic systems

This paper seeks to use robots' kinematic redundancy to excite the system persistently, through actively designing a secondary task in the null space of a primary task. Resulted convergence of unknown parameters in adaptive control leads to better system stability and performance. A measure in Grassmannian, referred to as Subspace Discrepancy Measure (SDM), is proposed for evaluating the additional benefit from the secondary task in converging unknown parameters to their true values. This measure evaluates the angles among subspaces that the parameter estimations are converging to, given different secondary tasks. The subspaces are obtained from Principal Component Analysis (PCA) on a small amount of samples of parameter estimations. The SDM is used to determine the choice of the secondary task online through a trial-and-evaluation procedure actively. Numerical simulations demonstrated that the secondary task chosen by SDM enhances the parameter convergence.