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An Adaptive Impedance Control Algorithm; Application in Exoskeleton Robot

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An Adaptive Impedance Control Algorithm; Application in Exoskeleton Robot Scientia Iranica B (2015) 22(2), 519{529 Sharif University of Technology Scientia Iranica Transactions B: Mechanical Engineering www.scientiairanica.com Research Note An adaptive impedance control algorithm; application in exoskeleton robot M.M. Ataei, H. Salarieh and A. Alasty Department of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran. Received 1 December 2012; received in revised form 10 May 2014; accepted 11 August 2014 KEYWORDS Abstract. Exoskeleton is a well-known example of an unconstrained robot for which the desired path is not prede ned. Regarding these two e ective features, a formulation Adaptive control; for impedance control algorithm is presented and its prominence is demonstrated both Impedance control; mathematically and through simulation. Moreover it is essential to control this robot by Modeling; an adaptive method because at least dynamic characteristics of the load are unknown. Exoskeleton. Unfortunately the existing methods do not address aforementioned traits or become unstable as inertia matrix becomes singular. Here an adaptive algorithm is generated based on the logic of Least Squares identi cation method rather than the Lyapunov stability criterion to tackle those limitations. © 2015 Sharif University of Technology. All rights reserved. 1. Introduction oskeleton manufactured by Sarcos Company which uses Impedance Control (IC) system. This method Exoskeleton is worn like a cover and enhances physical does not cause any of the mentioned insucien- might via powerful actuators. To accomplish this, cies. it constitutes of anthropomorphic parts which follow IC introduced by Hogan in 1985, was specially cre- movements of body simultaneously. A review on the ated to control the interaction dynamics of robot with major projects in this eld shows that researchers human or environment. But exoskeleton application have chosen various control methods [1]. BLEEX has three important features which a ect impedance project by Kazerooni is among the premier robots of control formulation: this kind (Figure 1). Its control method is based on measuring forces exerted on the robot's links and This robot does not have a speci c end-e ector and producing a control law to reduce those forces [2]. interacts with body at several points; Disability to distinguish between voluntary and invol- Exoskeleton cannot be treated as a constrained untary movements is a major disadvantage of that robot; method. Sankai developed HAL robot and utilized EMG sensors to detect intention of the user [3]. The desired path or equilibrium points are not These sensors need to be attached on the skin and predetermined. cause discomfort to the user. XOS is another ex- In a few articles IC is applied to exoskeleton, some of which use an admittance model to calcu- late desired movement and impose position control *. Corresponding author. Tel.: +98-21 66165538; to reach that goal [4,5]. In this way tracking qual- Fax: +98-21 66000021 E-mail addresses: [email protected] (M.M. Ataei); ity will be dependent on the working point that is [email protected] (H. Salarieh); [email protected] (A. not desirable. Caldwell et al. [6] employed IC for Alasty) a rehabilitation robot and assumed negligible veloc- 520 M.M. Ataei et al./Scientia Iranica, Transactions B: Mechanical Engineering 22 (2015) 519{529 2. Impedance control method 2.1. The algorithm From 1985 that Hogan explained impedance control in [10], supplementary issues about it were also dis- cussed till around 2000. Adaptation is among those issues. According to the viewpoint of the mentioned ar- ticle that aims industrial robots, the desired impedance relation is considered as: Mde + Cde_ + Kde = f; e = x xv; (1) where f represents interface force and x, xv are true and virtual positions of the end-e ector in its task space. The coecients of desired impedance are shown with index d and correspond to mass, viscous damping and sti ness. In situations that end-e ector is con- strained to move in contact with a speci c solid surface, Figure 1. BLEEX (left) and XOS (right) robots [2]. the desired path is known beforehand. Accordingly xv is determined by designer such that desired force is produced at the interface. In some other applications ity and acceleration. Besides they assumed that xv may represent an equilibrium trajectory around the desired inertia impedance factor is equal to the which the dynamics of the end-e ector would obey robot's inertia matrix. These assumptions eliminate Eq. (1). However our application is none of the above. complexities to develop control law but downgrade xv is replaced by desired position in [11], which is performance of control system in an actual applica- a well-known reference for robot dynamics and control tion. All of the mentioned works have simulated topics. Therefore if we have the dynamic equation of their method on a very simple model of one DOF. the robot as: In this research a formulation of IC suitable for any application like exoskeleton is presented, and after M(q)q + C(q; q_)_q + G(q) = + J T (q)f; (2) modeling a robot entirely the methods are applied on the model. where J is the Jacobian matrix and transfers local Already several adaptive methods for IC exist. coordinates q to the task space, the control law and In [7] model-reference adaptive methods for force con- closed-loop dynamics are respectively given as: trol, impedance control and combination of them both are presented but linear reference model is assumed = J T f + G + Cq_ for the plant while many systems like exoskeleton are highly nonlinear. In [8] another model-reference 1 T + M(qd Md Cde_ + Kde + J f ); (3) adaptive impedance control algorithm for constrained robots is developed but it is not useful for uncon- Mde_ + Cde_ + Kde = f; e = q qd: (4) strained ones like our robot. Lu and Meng [9] have presented two adaptive IC algorithms which were Here qd represents desired trajectory. So this method originally developed by other researchers, and they needs both f andq d to produce the control law. But employed and enhanced these methods in IC. These in an application that the desired trajectory is not methods give the best performance quality and do predetermined, there is no means to obtain desired not have the mentioned problems but still face a path except calculation through desired impedance limitation. relation. By a little change in representation of IC Adaptation laws in these methods need inverse of concept, it is possible to attain the desired impedance the inertia matrix while in many cases this matrix is dynamics without the mentioned calculation. More always or for some states singular. Here we present an important point is that the nal consequence of the adaptive Impedance Control (IC) method based on the above formulation, as in Eq. (4), does not guaranty Least Squares (LS) logic instead of Lyapunov stability. convergence of error and its rst and second time This yields an adaptation law with no need to calculate derivatives to zero, because the interface force on the inverse of inertia matrix. Besides, a representation right hand side of this equation acts as a disturbance of impedance control is introduced which enhances itself. Only when the interface force becomes zero the performance of IC and ts the special features of error between the desired and actual states converges exoskeleton discussed previously. to zero. M.M. Ataei et al./Scientia Iranica, Transactions B: Mechanical Engineering 22 (2015) 519{529 521 In an application like exoskeleton that the desired Remark. In fact considering the di erence of q and path is not predetermined, qd should be calculated q0 enables us to distinguish between two issues: One from Eq. (4) and this needs q and its derivatives to be concept is user's intended deviation from the present measured via sensors. So for example theq measured to position () that is desired, while the other concept calculate qd and consequently to produce control law, is deviation of position that robot reaches to by is di erent from theq obtained from dynamic Eq. (2) obeying control law from the desired position, which which itself is dependent to the control law. To remove is error and should converge to zero as fast as possible. this ambiguity we name the measured position signal Clari cation of this separation in the theory makes by q0, and the position signal derived from dynamic it possible to design control law such that the right equation using control law is depicted by q. Therefore side of error dynamics becomes zero while interface the desired impedance relation is rewritten as: force exists and is considered in the desired impedance relation. This makes error and its rst and second _ Md + Cd + Kd = f; derivatives to approach zero quickly. The e ect of this is revealed in decreasing the interface forces exerted on = qd q0: (5) the user. Simulating the common IC formulation and the Assuming equality of q0 and q, is mathematically possible but physically impossible as in [11]. However, one presented in this article on a simple plant shows ignoring this di erence does not cause that formulation the advantage of the proposed method. not to work, but will cause some errors which may 2.2. Simulation usually be neglected. Making small changes in IC A mass-spring-damper system equipped with a linear algorithm, we can reduce those errors to some extent double acting actuator is considered (Figure 2). Two and upgrade its performance. mentioned IC methods are simulated on this plant and Before calculating the closed loop dynamics, it the results are shown. should be noted that each link of this robot has First, for applying common method it is assumed interface with body and its state should be controlled.
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