Smoothing stability roughness of a robot arm under dynamic load using reinforcement learning

We introduce in this paper a new fractal/rough set modeling approach to the domains of attraction of nonlinear systems obtained by cell mapping. The state space is partitioned into cells and the stability regions found using cell to cell mapping. Our new approach gives a fractal rough set identity to the domains of attraction where cells are identified according to their fractal dimension as fully stable, possibly stable and unstable. There the stability domain is a rough set where fully stable cells determine the lower approximation of the domain, and possibly stable cells its rough boundary. Consequently, the totality of these cells forms an upper approximation to the rough stability domain. The boundary of this domain which is a rough set of cells having a fractal dimension as an attribute of roughness is smoothed, minimising the inherent stability uncertainty of the region, using a reinforcement learning technique which takes into account the stability history of each fractal/rough cell. This new approach intended to reinforce the performance of a controller under stability uncertainty is applied for illustrative purposes to a two-axis robot arm under dynamic load.