Nonlinear Adaptive Partial State Feedback Trajectory Tracking Control of Tendon Driven Robot Manipulators Beytullah Okur, Erkan Zergeroglu, Enver Tatlicioglu, Orhan Aksoy Abstract— In this work, the link position tracking control problem of a tendon driven robotic system is studied in the presence of parametric uncertainty and lack of velocity measurements both of links and actuators. A partial state feedback nonlinear adaptive controller is proposed to deal with the unmeasurable states and uncertain dynamical system parameters. A backstepping approach has been utilized to develop the control strategy. The proposed nonlinear tracking controller utilizes online update laws to adapt for parametric uncertainties, and requires only link and actuator position measurements and tendon tension measurements. Need for link velocity measurements are eliminated by using a nonlinear filter, and a set of linear filters is designed to estimate the actuator velocities. Lyapunov based arguments have been applied to prove the stability of the closed–loop system and semi–global asymptotic link position tracking is achieved. I. I NTRODUCTION Separating the actuators from the links of the robot and actuating each joint remotely would decrease the link size, mass and inertia of the robot manipulator. As this might become a key point in light weighted, agile robot design, a significant amount of research has focused on remotely actuating robotic systems. Among other remote power trans- mitting methods, the use of tendon transmission systems present less noisy, clean, and shock absorbent characteristics. Therefore, tendon driven mechanisms have been used in many robotic applications. To name some; [1], [2], [3] can be given as examples to small size applications such as robotic hands, and [4], [5], [6] are some examples for large size manipulators. The use of tendon driven actuation is more popular in dexterous hands [2], [3], [7] as the resultant task space motion in robotic hand design usuually does not need to be accurate. For applications where the main performance criteria is to accurately track a desired task space trajectory, the use of tendon driven mechanisms are limited which is mostly due to the elastic nature of the tendons where accurate position control and trajectory tracking becomes difficult. And in most model based controllers, it is necessary to include the elastic tendon dynamics to the system model, however, with this inclusion, the control problem becomes This research is supported by Grants of the Scientific and Technological Research Council of Turkey, TUBITAK Project No: 112E561. B. Okur is with the Department of Mechatronic Engineering, Yildiz Tech. University, Besiktas, Istanbul, Turkey. okur@yildiz.edu.tr E. Zergeroglu and O. Aksoy are with the Department of Computer Engi- neering, Gebze Institute of Technology, 41400, Gebze, Kocaeli, Turkey. ezerger@bilmuh.gyte.edu.tr E. Tatlicioglu is with the department of Electrical and Electronics Engineer- ing, Izmir Institute of Technology, Izmir, 35430 Turkey enver@iyte.edu.tr more complicated due to the extra dynamics and hence possible extra uncertainties [5]. Some part of past research has focused on designing controller for tendon driven systems. For some background on tendon driven robot manipulators and classical linear control approaches on tendon driven systems, the reader is referred to [8], [9], and the references therein. Controller formulations including system dynamics are limited in the literature. In [5], Kobayashi and Ozawa presented an adaptive neural network based controller for tendon driven robotic mechanisms with elastic tendons. In [10], Nakayama and Fujimoto tackled the tracking control of tendon driven robots by applying the delayed reflexive force feedback. In [11] and [12], Haiya et al. proposed controllers for multiple degree– of–freedom (dof) tendon mechanisms using nonlinear springs with hysteresis characteristics like stiffness adjustable ten- dons. For the proposed controllers, error of the equation of spring was estimated by a disturbance observer and compensated by utilizing the estimated disturbance. In [13], Wimbock et al. proposed an application of the Immersion and Invariance type framework to tendon driven systems with variable stiffness. Among the above cited work, the only work that considered the uncertainties in the system dynamics was given in [5], however the proposed adaptive controller required the measurement of the second and third time derivatives of link position measurements (see assump- tion (2) of [5]) which are usually not available. In this study, we design a nonlinear model based partial state feedback adaptive controller for tendon driven robot manipulators that does not require neither acceleration mea- surements nor velocity measurements. The proposed con- troller only requires link and actuator position measurements and tension measurements of each tendons. Specifically, the proposed semi–global adaptive partial state feedback trajec- tory tracking controller deals with parametric uncertainties via three different parameter update rules. The need for link velocity measurements are eliminated by utilizing a nonlinear link velocity filter during the error system development, and the lack of actuator velocity measurements have been overcome with the help of a set of linear filters. Adding the dynamics of the power transmission system and consider- ing tendon elasticity yield a complicated dynamic model, and the resulting system dynamics mandates the use the backstepping technique twice. After fusing the backstepping design procedure with Lyapunov–type analysis tools, we design the auxiliary backstepping control inputs, and the control input applied to the actuators. The stability analysis ensures boundedness of all the signals under the closed–loop 2014 IEEE Conference on Control Applications (CCA) Part of 2014 IEEE Multi-conference on Systems and Control October 8-10, 2014. Antibes, France 978-1-4799-7409-2/14/$31.00 ©2014 IEEE 228