Aerospace Science and Technology 15 (2011) 353–365 Contents lists available at ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte Optimal task space control design of a Stewart manipulator for aircraft stall recovery Ashraf Omran a,∗ , Ayman Kassem b a Department of Aerospace Engineering, Old Dominion University, Norfolk, VA, USA b Department of Aerospace Engineering, King Fahd University, Saudi Arabia article info abstract Article history: Received 16 December 2008 Received in revised form 14 August 2010 Accepted 17 August 2010 Available online 21 August 2010 Keywords: Stall recovery Stewart kinematics Dynamics Optimal control Genetic algorithms This paper presents an algorithm to develop a mission-based optimal task space control for a Stewart manipulator. The proposed algorithm consists of two optimization phases. The first phase seeks an optimal polynomial approximate model for the forward kinematics of a Stewart manipulator using a predicted square error cost function. The second phase optimally tunes the controller gains in order to meet special mission requirements. Genetic algorithms are used in both phases as the optimization method. A stall recovery maneuver, one of the most dangerous flight conditions, is selected as the test case. The proposed mission-based optimal task space control shows the capability to reduce the error in training the pilot for stall recovery maneuver.  2010 Elsevier Masson SAS. All rights reserved. 1. Introduction A stall, as a threat to safe flight, is a condition in aerodynamics and aviation where the angle of attack increases beyond a certain point such that the airflow starts to separate and lift begins to de- crease dramatically. Usually, the stall scenario starts by turning the thrust off, known as gradual stall, or by a sudden change in the el- evator deflection, known as abrupt stall. If the pilot fails to execute the proper recovery or delays his action, the aircraft may develop a high-risk sink rate or roll off into a spin with a high possibility of a ground impact. In this case, the pilot requires adequate training by practicing the recovery technique many times on flight simu- lators before trying to execute such maneuvers on a real aircraft [1,27]. As an elegant design for simulating flight conditions for training pilots, in 1965, Gough Stewart proposed a mechanical linkage with an octahedral assembly of struts that enables a platform to move simultaneously in all six degrees of freedom, three translational motions (surge, sway, and heave) and three rotational motions (pitch, roll, and yaw) [28]. The acceleration forces of this move- able plate can emulate the physical feeling of piloting an aircraft in forward, backward, or turning motions. As shown in Fig. 1, the moving plate is connected to the base plate by six legs. A spheri- cal joint is employed to connect the upper part of each leg to the movable plate, while the lower part is connected to the base plate * Corresponding author. E-mail address: aomra001@odu.edu (A. Omran). by a universal joint. Each leg has an upper part telescoping in- side a lower part by an independent electric or hydraulic actuator through a prismatic joint, where the lengths of these legs change the position and orientation of the platform. Because of the high force-to-weight ratio, accuracy, and rigidity, Stewart manipulator’s applications were not limited to a flight simulator only, but also included some other technologies such as machine tool, crane, un- derwater research, air-to-sea rescue, satellite dish positioning, and telescopes. This widespread applicability of Stewart mechanisms leads to an on-going research on its dynamics and control [28,29, 10–22,24–26,4–6,8,2]. Two control architectures are commonly used for a Stewart ma- nipulator: joint space control [25,26,29,17] and task space control [14,11]. The joint space control architecture is developed by con- trolling each leg as a single-input single-output (SISO) system. The error between the actual and desired joint position is used as a feedback signal to the controller. Although the joint space control has a simple structure because there is a closed form solution for the inverse kinematics model of a Stewart manipulator, this control scheme is unable to provide a high tracking performance in the case of a high amplitude maneuvers such as stall recovery. A joint space control doesn’t account for the dynamic coupling of the ma- nipulator. On the other hand, task space control accounts for the dynamic coupling of the manipulator, where the measures of joint space are mapped into a task space through direct kinematics. The task space control is exacerbated by the fact that the forward kine- matics of a Stewart manipulator has no unique solution. Dietmaier [5] has addressed 40 possible solutions. There have been several attempts to solve the forward kinematic problem using combined 1270-9638/$ – see front matter  2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ast.2010.08.009