Stratégie de commande distribuée pour les manipulateurs rigides et flexibles assurant la stabilité des erreurs de suivi de trajectoires

Abstract

This thesis studies and proposes a distributed nonlinear control strategy for rigid and flexible manipulators ensuring the stability of the tracking errors in the joint space and workspace. First, this strategy is applied to rigid manipulators. Then, it is modified and extended to take into account the links’ flexibility of flexible link manipulators. For the rigid manipulators, the control strategy is used to ensure a good tracking in the workspace. When the system parameters are perfectly known, a distributed control strategy is developed. First, this control strategy decomposes the dynamical model into a set of nonlinear interconnected subsystems. Each subsystem has one joint. Then, this distributed control strategy consists of controlling the last joint while assuming that the remaining joints are stable. Then, going backward to the next to the last joint, the same strategy is applied and so on until the first joint. When, the system parameters are unknown, an adaptive version is developed. In this case, the distributed and adaptive control can be interpreted as an hierarchical control. Indeed, the unknown parameters existing in the equation of motion of last subsystem are first estimated and the control is developed using this estimated parameters. Then, going backward to the before last joint, the control law is developed using its own estimated parameters and the ones already estimated in the upper level subsystem. The adaptive control strategy consists to control one subsystem in each step starting from the last subsystem. The same procedure is used, backward to the first subsystem. Global stability of the error dynamics is proved using Lyaponov approach. The proposed approaches are implemented in real time on a 7 DOF ANAT robot. Experimental results show the effectiveness of the approach and good tracking performance in the workspace. For the flexible manipulators, the above control strategies are modified and extended to solve the tracking control problem and minimizing vibrations of the flexible links. In this case, the control problem is twofold: in addition to motion objectives as in a rigid manipulator, it must also stabilize the vibrations that are naturally excited. The number of controlled variables for a flexible-link manipulator is strictly less than the number of mechanical degrees of freedom, i.e. it represents an under actuated system. For flexible link manipulators, each subsystem has a pair of one joint and one link. In the joint space, a distributed control strategy, based on the one proposed for the rigid manipulators, is developed when the flexible link manipulators parameters are known. An adaptive version or hierarchical control strategy is also deduced to track the desired trajectories and reducing vibrations of the links. These algorithms were tested on a two-flexible-link manipulator and gave effective results, a good tracking performance, and capability to eliminate the links’ vibrations. For the workspace tracking of flexible link manipulators, the inverse kinematics, used for rigid manipulators, is not sufficient to transform the desired trajectories from the workspace to the joint space. There exist two relationships between the workspace and joint: a kinematics and dynamics relations. To overcome this problem, an intermediate space, called virtual space, and quasi-static approach are used. Indeed, the inverse kinematics is used to transform the desired trajectories from workspace to the virtual space and the quasi-static approach is used between the virtual space and the joint space. The flexible links manipulators are non-minimum phase system when controlling the position of the endeffector. To solve the non-minimum phase problem, an output redefinition technique is used. This output consists of the motor’s angle augmented with a weighted value of the links extremity. The distributed control strategy consists in controlling the last link by assuming that the first link is stable and follows its desired trajectories. The control law is developed to stabilize the errors dynamics and to guarantee bounded internal dynamics such that the new output is as close as possible to the tip. The weighted parameter defining the non-collocated output is then selected. The same procedure is applied to control and stabilize the first link. The asymptotical stability is proved using Lyapunov theory. The control strategies are applied to a two-flexible-link manipulator in horizontal plane and simulations results showed a good tracking of the desired trajectory in the workspace.

Date	3 May 2013
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Maarouf Saad (Supervisor) & Mohamad Saad (Co-supervisor)