Maximum Spectral Flatness Control of a Manipulandum for Human Motor System Identification

System identification of a dynamic environment using a robotic device utilizes physical perturbations in the form of displacement or force. To obtain an accurate system model, physical perturbations must be informative, which can be characterized by their spectral properties. The process of generating physical perturbations by using a robotic device often leads to spectral property degradation in the high-frequency region due to the dynamics of robot motion control and discrete-time signal processing. Spectral flatness is a metric applicable to quantifying the fidelity of the robotic system and quality of physical perturbations on an external object. This letter introduces a new metric named Band-limited Spectral Flatness Gain (BLSFG) to evaluate the physical perturbation quality relative to the input reference over a frequency band of interest. Motion control of a manipulandum that generates pseudorandom position perturbations for human sensorimotor system identification is considered as a representative example. The closed-loop system dynamics of the position control is characterized and optimized based on the BLSFG. Results suggest that a certain underdamped closed-loop property is advantageous to improve the spectral flatness of a degraded continuous-time pseudorandom reference. A high BLSFG is achieved when the resonance frequency of the closed-loop system is close to the update frequency of the pseudorandom sequence.