Tip position control of flexible manipulators through visual servoing

Abstract

Visual servoing of eye-in-hand flexible manipulators is considered in this paper. Dynamic effects of both the rigid and the flexible motion of the manipulator are fully taken into account in a control solution where the two-timescale nature of the problem is exploited. The visual information is used in the “slow” subsystem for a task space oriented control law. Some simulation results finally show the effectiveness of the proposed controller. Introduction When high performance position control of a manipulator is considered, the use of visual feedback can considerably improve the precision of the end effector positioning. Visual information, unlike standard mechanical sensors such as encoders or strain gauges, yields a direct measurement of the tip position, avoiding estimation errors due to a rough knowledge of the physical parameters. These and other reasons have increased, in recent years, the interest towards the control of robots by means of visual feedback (so called visual servoing [1]). The precision enhancement, due to a direct measurement of the tip position, is even more significant if lightweight flexible manipulators are considered. In fact, the flexibility of the materials makes an accurate indirect estimation of the tip position extremely difficult, while a local position feedback at the end effector can circumvent these difficulties, at the expense however of an increase in the complexity of the control scheme. This paper deals with the eye-in-hand Image Based Visual Servoing of lightweight flexible manipulators with an approach that is inspired by the two-timescale control of flexible structures [2] and by the well-known task space control [3]. In fact, the problem of damping out the vibrations can be faced using a composite control technique [2]. With this approach the design of a feedback controller can be effectively split into two separate design problems: a fast feedback to stabilize the oscillatory dynamics and a slow nonlinear feedback to ensure that the actual image features asymptotically reach the prescribed desired ones. On the other hand, since a strict requirement of the composite control theory is to design the slow controller so that the timescale separation is preserved, a newly conceived approach, inspired by the computed torque controller, is here developed. Simulation results are finally presented, focusing on the model of a two link planar flexible manipulator. The two-timescale visual servo controller has been tested considering a target made up by two object feature points and described by a single feature segment. Robotic system model Flexible manipulator dynamics Considering a truncated modal approximation, under the assumption of small deflections of the links, the equations of motion for a flexible manipulator can be derived using a recursive Eulerian-Lagrangian approach [4]. The dynamic model of a manipulator with n flexible links can thus be written in the following form