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Top1. Introduction
The mechanical arm is a mechanical device that includes bases, joints, links and manipulator (H. W. Lee, 2020). At present, it has been widely applied to perform various production automation processes in industry since past tens of years (Yang et al. 2016; Zeng et al., 2019). On the other hand, the manipulator is the key component to be used in moving objects or materials, working similarly to a human hand. To accurately control the manipulator moving route, the straight-line trajectory planning is the most crucial task. For this demand, Bresenham algorithm is known as a common linear drawing model in linear trajectory planning (Zhang et al. 2015). Currently, it still has many applications in various fields. For example, Bresenham algorithm combined with the symmetry nature of lines can effectively improve the rasterization speed in image processing5. In the robotic arm drawing, the Bresenham algorithm was used to generate circular trajectories for achieving a better tracking of geometry (Mahmoud, et al. 2016). In the unmanned aircraft system (UAV), the initial path line can be obtained by the combination of Digital Elevation Map (DEM) with Bresenham algorithm, and Béziercurve is then used to smooth the lining path (Liang, et al. 2017). Beside, an advanced grid projection algorithm in navigation was further developed using Bresenham’s rasterizing algorithm (Kim, et al., 2014). In the 3D scene construction, Bresenham's line algorithm was applied to create 3D line segments from the sensor position to all points. The noise caused by a moving object can be eliminated in the current frame (Chu, et al. 2016). In the human vision application, a rehabilitation low vision algorithm based on the Bresenham algorithm was proposed to extend the user's visible area, covering the invisible hidden area of the human eyes (Fardoun, et al. 2013). In the agriculture automatic seeding, some line precision methods using the Bresenham algorithm may determine the precise location of automatic watering and seeding functions (Lian, et al. 2020). The conventional Bresenham straight line algorithm was also adapted in path generation and control of a hydraulically actuated tunneling robot (Zsombor-Murray, et al. 2005). However, a certain amount of complex mathematical function like square roots and floating-point operations is needed to perform.
As above, it indicates that Bresenham algorithm can work well in a straight-line or path planning, also avoiding the error caused from computation. Nevertheless, it may suffer from the abrupt speed changing of the mechanical arm during starting and braking period. Accordingly, the Bresenham algorithm combined with step compensation method for optimization is developed for a linear manipulator trajectory planning in this study. In Section 2, the fundamental of Bresenham algorithm is introduced. It demonstrates how the moving path in space can be a straight-line with the shortest distance. In Section 3, the step compensation optimization method combined with Bresenham algorithm is proposed. It is focused on the reduction of the starting speed by setting up different insertion point densities, which can improve the speed mutation problem and maintain the benefit of Bresenham algorithm. The conclusions are presented in Section 4.