Control Applications

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Control Theory and Applications

The academic background of the Robotic Systems Control Laboraoty is control theory, in particular robust and adaptive control theories. The direct applications of the control theory research include the following specific topics:
A. Controller Design for Mechanical Impedance Reduction
Mechatronic systems that physically interact with humans should guarantee safety, as well as stability and control performance. Mechanical impedance is an effective means to evaluate the safety of such systems. The mechanical impedance represents the magnitude of reaction forces by mechanical system when it is moved. Therefore, low mechanical impedance is one of the requirements of safe mechatronic systems. However, there exists a tradeoff between mechanical impedance, stability, and control performance. In this research, a methodology to design control algorithms for reduction of the mechanical impedance with guaranteed stability is proposed. For the controller design, the mathematical definition of the mechanical impedance for open- and closed-loop systems is introduced in this research. Various analyses on the mechanical impedance from the viewpoint of control systems are given. Then, the controllers are designed for systems with/without right-half complex plane poles and zeroes such that they effectively lower the magnitude of mechanical impedance with guaranteed stability. The proposed method is verified through case studies including simulations and experiments.

Impedance Reduction Control
B. Frequency-Shaped Impedance Control for Safe Human--Robot Interaction in Reference Tracking Application
In the control of industrial robots, both safety and reference tracking performance are required. For safe human-robot interaction, robots should exhibit low mechanical (or controlled) impedance so that they react to the interaction forces in a compliant manner. On the other hand, the reference tracking requires for the robots to reject exogenous disturbances, which results in an increased impedance. In order to achieve these two conflicting objectives, a frequency-shaped impedance control (FSIC) method is proposed in this research. The proposed method utilizes the two different functionalities of the disturbance observer (DOB): a disturbance estimation function as an observer and a disturbance rejection function as a feedback controller. Namely, the DOB is utilized as an observer at the frequencies where the robots interact with humans, while it is used as a feedback controller (i.e., disturbance rejection controller) at the frequencies where the reference tracking is required. The proposed approach is realized by shaping a filter of the DOB in the frequency domain so that the impedance is manipulated to achieve both the compliant interaction and reference tracking. The compromised reference tracking performance in the frequency range, where the impedance is set low, can also be supplemented by feedforward control. A typical feedback controller and a feedforward controller are designed in addition to the DOB-controlled system as the whole control system to enhance reference tracking performance and the betterment of stability robustness. The proposed method is verified by experimental results in this research.

Frequency-Shaped Impedance Control
C. Real-time Nonlinear Programming
In this research, a complementary method that optimizes an arbitrary multi-variable cost function in real-time is proposed. Taking the advantages of both NLP and ESC, the variables are updated by the steepest descent method of NLP, while the gradient of the cost function is continuously estimated by the amplitude modulation as in ESC. Unlike the ESC, the proposed method does not require the design of complicated filters. The optimization performance is verified by simulations on time-varying and noisy cost functions, as well as automatic controller tuning applications.

Simulation of Real-Time Nonlinear Programming on two-dimensional noisy cost function;
(Left) without noise, (Right) with Gaussian noise.