A comparative study of H∞ and PID control for indirect deformable object manipulation

Manipulation of deformable objects is a field of research that has a variety of applications, including medical procedures, food industry, and manufacturing. This paper compares the performance of a standard PID controller and a robust H_∞ controller, both of which are designed to perform the task of indirect deformable object manipulation. The H_∞ controller is generated using methods outlined by Doyle et al., and the PID controller is tuned in a conventional trial and error approach. Unmodelled dynamics of the deformable object system are considered disturbance inputs and compensated by both controllers. Loop shaping is used to model the robotic actuators and position feedback system limitations within the process of generating the H_∞ controller. The H_∞ proved to be superior to the PID in both simulations and experiments. Maximal steady state error of the H_∞ controller was 0.5mm; PID maximal error was 1 mm at steady state. The key benefit of the H_∞ approach is that the controller generated using the numerical model of the deformable object performed well in simulations and experiments; the parameters of the PID controller required retuning between simulation and the experimental setting.