In this paper we show how the design of robust robotic systems can profit from the emerging research field of organic computing by bringing together adaptive systems theory, controller design, and fault tolerance. In particular, we have evaluated in a case study of a hexapod walking robot the use of linear adaptive filters for the detection and correction of faults. Our analysis shows that linear filters can be applied for monitoring the system state and a simple threshold approach utilizing the weights of the adaptive filter can be exploited for fault detection. This even holds in the case of using additional adaptive filters for direct fault compensation in the controller loop. We present the case study and our experimental results which have been derived in a Matlab simulation.