A Preliminary Study for H\(_\infty \) Control of Parallel Cable-Driven Manipulators
This paper reports preliminary investigations for H\(_\infty \) control of cable-driven parallel robot. This methodology specially suits for multi-input multi-output systems including flexible modes, which is the case of cable robots with flexible cables.
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bstract This paper reports preliminary investigations for H∞ control of cabledriven parallel robot. This methodology specially suits for multi-input multi-output systems including flexible modes, which is the case of cable robots with flexible cables. A nonlinear model is first developed accounting for flexible cables for the case where actuators are speed controlled. A first method based on a rigid model is proposed as an adaptation for speed-controlled actuators of the well-known Jacobianbased method. A low-pass filter is tuned in order to increase the reachable bandwidth. The H∞ controller is derived from a linear dynamic model. One interest is that one single controller manages both the position of the end-effector and the cable tension. The simulation results show that improvements are possible in the bandwidth thanks to the H∞ control.
1 Introduction Cable-driven parallel robots have several advantages that make them an attractive solution for several original application field. Thanks to their large operation range, they allow to move a camera over an operation field such as astadium (see the
E. Laroche (B) · R. Chellal · L. Cuvillon · J. Gangloff LSIIT laboratory, Strasbourg university and CNRS, Strasbourg, France e-mail: [email protected] R. Chellal e-mail: [email protected] L. Cuvillon e-mail: [email protected] J. Gangloff e-mail: [email protected] T. Bruckmann and A. Pott (eds.), Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, DOI: 10.1007/978-3-642-31988-4_22, © Springer-Verlag Berlin Heidelberg 2013
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Cablecam company, http://www.cablecam.com/). Their low invasiveness and potentially high safety make then good candidates for interactions with human operators, such as in medical robotics [1]. When dealing with control, several items must be considered: • As any parallel manipulator, kinematic constraints must be managed by the control law. • Their main default is common with all the flexible manipulators: due to the elongation of the cables, a control at the joint level cannot ensure an accurate positioning of the end-effector level. Therefore, some exteroceptive sensor is necessary (see Dallej et al. for a prospective study of vision-based control of a cable-driven robot [6]). Several approaches have been proposed in the literature for the control of cable robots. To our knowledge, the first approach for handling the cable tension was proposed by Ming and Higuchi [14]. Zi et al. consider long cables and account for their geometry to derive a fuzzy controller [22]. You et al. use a backstepping approach to control a 3-DOF cable robot [20]. Alikhani and Vali use sliding mode to control a 3 DOF suspended crane and the second Lyapunov approach to show the stability of the control scheme [2]. Diao and Ma consider a model where the flexible effects are modeled as equivalent springs and analyses the flexible modes [7] but do not consider any control solution. H∞ control methodology has bee
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