Robust Control for High-Speed Visual Servoing Applications › publication › fulltext › Robust-Co... › publication › fulltext › Robust-Co...by LP Ellekilde · 2007 · Cited by 10 · Related articlesdefined directly in the image plane or in Cartesian space.
Abstract: This paper presents a new control scheme for visual servoing applications. The approach employs quadratic optimization, and explicitly handles both joint position, velocity and acceleration limits. Contrary to existing techniques, our method does not rely on large safety margins and slow task execution to avoid joint limits, and is hence able to exploit the full potential of the robot. Furthermore, our control scheme guarantees a well-defined behavior of the robot even when it is in a singular configuration, and thus handles both internal and external singularities robustly. We demonstrate the correctness and efficiency of our approach in a number of visual servoing applications, and compare it to a range of previously proposed techniques. Keywords: Visual Servoing, inverse Jacobian, Quadratic optimization
1. Introduction In recent years, much research has been aimed at developing control schemes, which enable robots to react to changing or uncertain environments. The main reason for this is that such methods not only will allow robots to be employed in applications, which are not feasible today, but also effectively eliminate the need for accurate workcell modeling and part fixturing as well as relax the accuracy and stiffness requirements for the robot. One control scheme that has been given special attention is visual servoing. In visual servoing, a visual feedback signal is introduced into the robot control loop and used to define a measure of positional and orientational error of the end-effector relative to a target object (Hutchinson, S.A.; Hager, G. & Corke, P.I., 1996). Performing such closed-loop visual control of the end-effector relative to the workpiece effectively enables the robot to perform successful tasking even in case of significant uncertainties in the workcell and/or in the kinematic model of the robot. Traditional visual servoing systems are categorized as image based or position based depending on whether the error computed from the visual measurements are defined directly in the image plane or in Cartesian space. More recently, several hybrid schemes, which attempt to eliminate drawbacks of the classical techniques, have been proposed (Malis, E.; Chaumette, F. & Boudet, S., 1999, Corke, P.I. & Hutchinson, S.A., 2000; Deng, L.; Janabi-Sharifi & Wilson, W.J., 2002). Common to all visual servoing approaches is however that the visual measurements are used to compute a sequence of desired velocity screws for the robot endeffector. These velocity screws are subsequently transformed into joint velocities using the inverse of a
International Journal of Advanced Robotic Systems, Vol. 4, No. 3 (2007) ISSN 1729-8806, pp. 279-292
robot Jacobian either derived from a known kinematic structure or estimated using iterative approximation methods (Paulin, M., 2004a). A well-known problem of this approach is that it accounts for neither kinematic singularities nor ensures that commands that violate joint position, velocity and acceleration limits are not attempted or executed. Several techniques, which utilize redundant degrees of freedom to resolve one or more of these issues, have been proposed. The Compact QP Method (Cheng, F.-T.; Chen, T.-H. & Sun, Y.-Y., 1992) by Cheng et. al. formulates it as a quadratic optimization problem with linear equality and inequality constraints in the joint velocity domain. The equality constraints contain the relation between the joint velocities and the Cartesian tool velocity, and insure that the solution always follows the specified trajectory. For redundant manipulators the inequality constraints can be used to model physical limits such as on joint position and velocities. Finally the quadratic term, can then be used to control the remaining degrees of freedom e.g. to steer clear of singularities. If it reaches a singularity there will be at least one degenerated direction. The task is therefore divided into a part in which the Jacobian has full rank, which is used as equality constraints, and a second part, which is incorporated in the quadratic objective function. In (Cheng, F.-T.; Sheu, R.-J., Chen, T.H. & Kung F.-C., 1994) it is shown how to improve the performance of the Compact QP Method by decomposing it into two subproblems. Extensions to incorporate quadratic constraints are provided in (Kwon, W.; Lee, B.H. & Choi, M.H., 1999). Within the visual servoing community the most widely used method seem to be the Gradient Projection Method (GPM) originally proposed in (Liegeois, A., 1977). GPM
279
International Journal of Advanced Robotic Systems, Vol. 4, No. 3 (2007)
defines a performance criterion as a function of joint limits and projects the gradient of this function onto the null space projection matrix of the interaction matrix, which relates sensor space velocities directly to joint velocities. This allows for generation of self-motions, which keep the robot away from joint position limits. Marchand et al. (Marchand, E.; Chaumette, F. & Rizzo, A., 1996) have proposed a similar technique, based on the task function approach (Samson, S.; Borgne, M.L. &
