Leader–follower formation control of four-legged robots with discrete-valued inputs

Abstract

This paper addresses a leader–follower formation control problem for four-legged robots under discrete-valued input constraints. Four-legged robots are more suitable for rough terrain missions than wheeled robots because the tip positions of their legs can be changed depending on the terrain. However, it is difficult to control these robots through continuous-valued inputs because they are steered by switching between specific movements (i.e., discrete-valued signals). Motivated by this fact, we have proposed controllers that achieve fixed formations of four-legged robots using discrete-valued inputs, but moving formations, which are necessary for some applications, have not been considered yet. Herein, we present a solution to the above leader–follower formation control problem based on the combination of PD-like formation controllers and dynamic quantization. We further introduce a performance index to evaluate the difference between two systems whose inputs are quantized and unquantized and analyze the index for the feedback system with the presented controllers. As a result, an upper bound of the performance index is derived as a function of the system parameters. This is useful to evaluate the impact of the quantization on the behavior of the feedback system and to provide a theoretical guarantee of the stability of the system.