Comprehensive Bond Graph Modeling and Optimal Control of an Anthropomorphic Mechatronic Prosthetic Hand Muhammad Tallal Saeed 1+ , Sardor Khaydarov 2+ , Biniam Legesse Ashagre 3+ , M. S. Zafar 4# + Department of Intelligent Systems and Control Engineering, Beihang University, Beijing, China # Department of Computer Science and Engineering, Beihang University, Beijing, China 1* talalsaeed@buaa.edu.cn, 2 sardor@buaa.edu.cn, 3 lbiniaam@buaa.edu.cn, 4 mszafar.dcs@outlook.com Abstract - This paper presents comprehensive modeling, simulation and optimal control of an anthropomorphic mechatronic prosthetic hand comprising of 20 DOF. To acquire the mathematical model of the robotic hand, the graphical modeling technique known as the bond graph has been used. Bond graph provides precise dynamic model of complex systems, with relatively fewer computations and ease as compared to other modeling techniques. Precise modeling leads to better control performance which is essential for prostheses. In this research, firstly, linear quadratic (LQ) controller has been designed for desired movements of fingers of robotic hand with optimal control energy. Secondly, the system is formulated as an H2 optimal control problem in which the Gaussian noise is introduced at the input and output and an optimal H2 controller is designed for system stability in the presence of noise. Graphical modeling is carried out by using the 20-sim software and the mathematical equations of the system are obtained. These equations are then imported to MATLAB ® where the optimal controllers have been implemented and simulated. The closed loop feedback dynamic responses of index finger (flexion and extension movements) for both the controllers have been presented and analyzed. The results show that the optimal controllers have provided the desired output in terms of stability. Index Terms - bond graph; dynamic model; Gaussian noise; linear quadratic; H2 optimal control; I. INTRODUCTION In the past few decades, extensive research has been carried out in designing and developing various types of robotic hands for different purposes [1, 2]. Employment of robotic hand as a prosthesis, has been very beneficial and has played an important role in improving the quality of life for the handicapped individuals. On the other hand, for the researchers and engineers in the field of bio-robotics, replication of human hand to imitate the natural features as closely as possible, has always been a challenging task. However, advancements in robotics technology have enabled them to fulfil the task more efficiently and effectively. Mechatronic robotic hands comprise of mechanical structure and electrical components and are electronically controlled to achieve desired movements. There have been numerous active anthropomorphic mechatronic robotic hands designed up-till now, comprising of compact and optimized structural designs and advanced control strategies [3, 4]. Both these aspects play a vital role in achieving the desired stability and performance of the system. Modeling, simulation and control of some robotic hands are presented in [4-6]. Mathematical model of dynamic systems is obtained using the modeling techniques and then the control strategies are applied. Precise model of the hardware exhibits the system behavior more accurately, which leads to better control performance. Moreover, while achieving model accuracy for complex systems, the order of the system increases, resulting in intricate computations. Modeling of complex systems through bond graph approach requires fewer computations and is more flexible as compared to conventional modeling methods. In this modeling approach, the physical systems are presented graphically, in which the subsystems are interconnected through bonds based on the flow of power in the system [7, 8]. This makes bond graph technique applicable for modeling multidisciplinary systems. To obtain a precise model, it is essential to have complete information about subsystem interconnections; and parametric values of the variables corresponding to the actual hardware components. Bond graph of a system can be made manually, and the system equations can be formulated. There is software for bond graph modeling known as 20-sim [9, 10] in which the graphical model of the system is generated, and the mathematical equations are obtained for system analysis. In this research, a robotic hand with five active finger movements is proposed, modelled and optimally controlled. For modeling purpose, the details of each hardware component have been presented and discussed. Bond graph is generated using 20-sim software and the mathematical model in the form of transfer function is obtained. To achieve optimal stabilizing controllers for dynamic response of the fingers of robotic hand, first the control problem is formulated as an LQ problem and a stabilizing controller using LQ regulator (LQR) is designed. Second, the control problem is formulated as H2 optimal problem by introducing Gaussian noise and H2 controller is designed to ensure stability in the presence of noise. Step and Impulse responses of the system for both the controllers are presented and analyzed. II. STRUCTURAL DETAILS OF ROBOTIC HAND The proposed robotic hand is an active mechatronic system and the architecture of the hand is anthropomorphic. Like the human hand, it comprises of four fingers and a thumb. Each finger and thumb comprise of 3 DOF for flexion (flex.) and extension (ext.) movements. The thumb, index finger and fourth finger have one additional DOF each for abduction (abd.) and adduction (add.) movements. 2006 978-1-7281-1699-0/19/$31.00 ©2019 IEEE Proceedings of 2019 IEEE International Conference on Mechatronics and Automation August 4 - 7, Tianjin, China