Predictive sensor guided robotic manipulators in automated welding cells

This paper presents an on-line tracking optimization scheme for sensor guided robotic manipulators by associating sensor information, manipulator dynamics and a path generator model. Feedback linearizationdecoupling permits the use of linear SISO prediction models for the dynamics of each robot joint. Scene interpretation of CCD-camera images generates spline fitted segments of future trajectory. In the sensor vision field the proposed optimization criteria minimizes the error between state variables of the prediction model and the state variables of the spline trajectory generator. These techniques, allied with separation of disturbance rejection and path-tracking performance by the proposed feed-forward Following Model Predictive (FMP) servocontroller design, permits very high path tracking dynamics (and consequently small errors). Experimental results on implementation of a CCD-camera guided hydraulic robot and a welding robot demonstrates the practical relevance of the proposed approach. Introduction Robotic manipulators have been used in welding cells for long time in order to improve welding quality. Substitution of mancraft in welding cells where a robot welds only few different parts every time in the same manner, such as in spot welding commonly used in the automobile industry, is not a very difficult task. But in a flexible, just-in-time, and CAD customized production approach, very different parts are to be welded demanding an "intelligent" robot-welding concept. Providing robots with abilities of an experienced welder is the visionary target of many research groups. The realization of such ambitious goal leads to the use of sensors, which provide the robot with the necessary information, so that it can interact within their environment. Preferentially, the robot should autonomously find and precisely weld metal joining paths in order to fulfill some given manufacturing task [1]. A shortcut of the use of sensor-guided robots is that due to their mechanical inertia they can react only relatively slowly to changes in the trajectory information captured by the sensor system. In this paper it will be shown how a sensor that can look ahead, such as a CCDcamera, can be used to improve substantially the seam tracking precision. The proposed algorithm virtually eliminates the tracking error by considering the dynamic model of the robot and the captured future trajectory information. Incorporating an internal trajectory generator model leads thus to the Following Model Predictive servo-controller algorithm (FMP for short [3]). Non-linear control techniques [6],[7],[12] can decouple and linearize robotic manipulator joints. So that each robot joint can be considered as a linear SISO system. Using such model, the tracking problem of sensor guided manipulators can be treated in the linear domain. In particular, the discrete optimization of the predictive pathtracking problem with the proposed cost function leads to an analytical solution with guaranteed stability [3],[11]. This new approach avoids the typical recursive solution usually employed for the Riccati equation [2]. Robotic manipulators equipped with sensors can automate industrial processes in an "intelligent manner". Those are objects of intense research efforts in the field of Artificial Intelligence (AI): to build machines that consider the information captured from the surrounding environment in a proper (intelligent) manner. With the support of sensors the working trajectory of the robot can be obtained within a certain vision field, which will be used here as the minimization horizon of the tracking error. The proposed algorithm was implemented to control a hydraulic manipulator guided by a CCD-camera, where it was showed that the FMP methodology significantly reduces the dynamic tracking error. Currently this technique is being implemented to control a 6-DOF CCDcamera guided welding robot at GRACO. Dynamic system tracking Depending on the characteristics of tracking the following classification of problems are usual, [2]: • The tracking problem: The reference trajectory is a determined (arbitrary) function of time for 0 < t < T. • The servo problem: The system is to be controlled in such a manner that the controlled variable will follow a reference signal from which it is only known that it belongs to a certain signal class, e.g. a sequence of steps or polynoms until a certain order. • The model following problem: The output of the servo-system should follow the output of a path generator. For sensor-guided robotic manipulators the tracking problem is to be solved, because the captured trajectory is not known a priori. For the model following problem it is possible to obtain ideal following, i.e. zero tracking error in every time instant [14]. A proper path generator for robotic manipulators is an integrator chain, which in the case of three chained integrators produce spline polynoms. The scheme to obtain ideal following for a linear SISO system in the controllable canonical form is shown in Figure 1. Figure 1 Scheme to obtain ideal following [14]. Despite ideal following can not be obtained for sensor guided manipulators, their basic idea will be used here: minimize the error between the state variables of the controlled system and the state variables of a path generator internal model. It is important to point out that, if the captured trajectory is indeed a spline, the theoretically FMP tracking error will be zero [3],[14]. Following Model Predictive path tracking Consider the controllable and observable scalar n-th order discrete time linear system described by: ), ( ) ( ) 0 ( ); ( ) ( ) 1 ( 0 k k y k u k k T k s k k x c x x b x A x = = + = + (1) where x(k) is the nx1 state vector at time t=kT (T is the sampling period), us(k) is the input and y(k) is the system output. This model, with n=3, will be used here for robotic manipulators that are linearized and decoupled by an underlying non-linear multivariable joint controller. The resulting integrator chain that is obtained, for example by the inverse system controller [6],[7] or by the controller of the highest derivative [12], is then transformed in a P-Tn system by means of linear state feedback. Finally the discrete model (1) is obtained using a Step Invariant Transformation [14]. That model will be here, therefore, denominated predictor model, because it allows the prediction of the dynamic behavior of each robot joint for a given reference trajectory. Problem formulation Given an n-th order plant described by (1). The reference trajectory and its derivatives w(t), ( ) ( ),... ( ) w t w t n−1 are known from t = (k+1)T until the horizon t = (k+m)T. The current state of the plant is x(k). The position, velocity, acceleration, and higher derivatives of the controlled variable correspond to the states of the system in the controllable canonical form. The problem consists on the calculation of the control sequence us(k), us(k+1), ... us(k+m-1), such that the following predictive path tracking Optimization Criteria (or Cost Function) will be minimized: J i T i i i n T = + = − ∑ε ε β β Q R 0 1 (2) The weighting matrices Qi and R are symmetric positive defined. In the most general case these matrices can be time dependent. The vector error terms εi are: Position Error: ε 0 ( ) ( ) ( ) k k k = − y w (3)