IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 2, APRIL 1999 445 Tracking Control and Trajectory Planning in Layered Manufacturing Applications Abderrahim Bouhal, Mohsen A. Jafari, Member, IEEE, Wen-Biao Han, and Tong Fang, Student Member, IEEE Abstract— This paper discusses the improvements acquired by the introduction of a tracking controller and a look-ahead trajectory-planning policy in part fabrication using the layer manufacturing process. The improvements are quantified not only in terms of tracking and contouring errors, but they are also quantified in terms of overfilled and underfilled areas, thus directly relating the quality of parts fabricated through such a process. Index Terms— Fused deposition, layered manufacturing, mo- tion control, software prototyping, tracking, trajectory planning. I. INTRODUCTION T HE layered manufacturing (LM) process significantly reduces part-specific setup manufacturing lead times. It has been primarily used in building prototypes for design con- ceptualization, verification, and simulation. As the application of LM expands from merely prototyping to functional parts, the fabrication of accurate geometry becomes an important issue. In the case of fused deposition modeling (FDM) the built process, which includes both the positioning and deposition processes, can be a potential source of defects. The errors generated by the built process are essentially due to the accumulation of the deposition errors and the – positioning errors. The current FD technology only supports open-loop positioning and deposition control systems. In the case of rapid prototyping, the open-loop control system does not necessarily impose much of a problem as the tolerance for the various geometrical and dimensional features of the part are relatively not so tight. This is no longer true if the technology is intended to be used for fabrication of functional parts [5]. The focus of this paper will be particularly oriented to tracking control and trajectory profile generation for FD technology. We intend to test our models on the FD machine that is under construction at Rutgers University, Piscataway, NJ. To evaluate the performance of the proposed approach, a simulation model has been developed for the positioning system. Section II presents an overview of the FD technology. The process model is given in Section III. The proposed tracking control strategy and the trajectory profile generation algorithm are respectively discussed in Sections IV and V-A. A program for the evaluation of underfilled and overfilled areas within Manuscript received December 9, 1997; revised September 25, 1998. Abstract published on the Internet January 18, 1999. This work was supported in part by the Office of Naval Research under Grant N00014-96-1-1175. The authors are with the Department of Industrial Engineering, Rutgers University, Piscataway, NJ 08855 USA (e-mail: jafari@rci.rutgers.edu). Publisher Item Identifier S 0278-0046(99)02723-9. Fig. 1. FD Process. a layer is discussed in Section V-B. A simulation model and results are given in Section VI for both contour and raster tool path patterns. II. FD TECHNOLOGY A. FD Process Description The FD process is an LM technique for the fabrication of polymer, wax, and ceramic parts using FD technique. The process starts by designing a boundary surface model of the part using a computer-aided design (CAD) package. The CAD model is then sliced [2] into a succession of horizontal layers ordered by their coordinates in the axis. For each layer, the boundaries of the slices are fabricated using a contour tool path, and the interiors are filled with a raster tool path pattern. The density of a raster pattern is controlled by the air gap between raster segments. The tool-path information and the design parameters are then merged into a design file and downloaded to the FDM machine. B. Machine Description An FDM machine [1], [9] consists essentially of a head liquefier (Fig. 1) attached to a carriage moving in the horizon- tal – plane. The function of the head-liquefier assembly is to heat and pump the filament material (polymer, wax, or ceramic) through the tip onto the modeling surface. The spooled filaments are fed into the liquifier via a set of two feedwheels driven in a counterrotating direction by a small dc servomotor which provides enough torque to the filament to act as a piston during the extrusion phase. The filament softens and melts inside the liquefier, and then it is extruded out of a nozzle tip located at the bottom end of the liquifier. 0278–0046/99$10.00  1999 IEEE