Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 7310105, 15 pages

https://doi.org/10.1155/2017/7310105

## A Synthetic Algorithm for Tracking a Moving Object in a Multiple-Dynamic Obstacles Environment Based on Kinematically Planar Redundant Manipulators

^{1}State Key Laboratory of Robotics and Systems, School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150080, China^{2}Aerospace System Engineering Shanghai, Shanghai 201109, China

Correspondence should be addressed to Hongzhe Jin, Ge Li, Yanhe Zhu, and Jie Zhao

Received 3 November 2016; Accepted 14 December 2016; Published 30 April 2017

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2017 Hongzhe Jin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a synthetic algorithm for tracking a moving object in a multiple-dynamic obstacles environment based on kinematically planar manipulators. By observing the motions of the object and obstacles, Spline filter associated with polynomial fitting is utilized to predict their moving paths for a period of time in the future. Several feasible paths for the manipulator in Cartesian space can be planned according to the predicted moving paths and the defined feasibility criterion. The shortest one among these feasible paths is selected as the optimized path. Then the real-time path along the optimized path is planned for the manipulator to track the moving object in real-time. To improve the convergence rate of tracking, a virtual controller based on PD controller is designed to adaptively adjust the real-time path. In the process of tracking, the null space of inverse kinematic and the local rotation coordinate method (LRCM) are utilized for the arms and the end-effector to avoid obstacles, respectively. Finally, the moving object in a multiple-dynamic obstacles environment is thus tracked via real-time updating the joint angles of manipulator according to the iterative method. Simulation results show that the proposed algorithm is feasible to track a moving object in a multiple-dynamic obstacles environment.

#### 1. Introduction

Planar manipulators can accomplish many tasks with high efficiency for a long time in specific/dangerous environments. Many researches have integrated vision technologies into manipulators system to further improve their intelligence, involving object perception, path prediction, action decision, path planning and execution, and so on [1–3]. The planar redundant manipulators with vision technologies can be used to inspect the facilities in complex environments or narrow spaces, such as ITER relevant inspection robots [4, 5] and SAFIRE robots [6]. The control systems of the redundant manipulators can be designed based on dynamics or kinematics [7]. The system based on dynamics has better real-time performance, but it heavily depends on the hardware system and the level of the designer. Besides, the hardware system is closed, which limits the further development. The system based on kinematics is open and easier to achieve a complicated motion of the manipulator via the upper planning. And such system plays key roles in realizing intelligent control of robot manipulator. So the focus of this paper will be devoted to the study of kinematically planar redundant manipulator.

Typical researches on the manipulators with vision system aim at real-time tracking moving objects in the varying environment. Allen et al. introduce a control algorithm to predict ahead the trajectory of the object in real-time, and the tracking can be performed by kinematic transformation computation [8]. Husain et al. present an automated system with a Microsoft Kinect sensor to track the moving object via reducing the distance between the object and the tripper mounted on the 7 degrees of freedom (DOF) robotic arm in real-time [9]. A simulation research, developed by Wei et al. [10], predicts the pose of the object in the next period by using the observed feature points at first; then the manipulator is controlled to achieve the real-time tracking. In [11], the authors propose an adaptive neuropredictive control method for redundant robot manipulators, which includes the prediction and obstacles avoidance, but the tracked path is planned offline and defined to be not affected by the dynamic obstacles.

Nevertheless, to track a moving object in a multiple-dynamic obstacles environment, several technologies must be considered at the same time, containing moving path prediction, path planning, and real-time obstacles avoidance. Moreover, these technologies must be synthesized reasonably to ensure that the moving object can be grasped successfully. In the literatures, however, although the existing methods have considered the prediction, path planning, and the obstacles avoidance, the failure of tracking always occurs in a multiple-dynamic obstacles environment. The main reason, on the one hand, is mainly due to the insufficient synthesis of these technologies. On the other hand, the impacts of the dynamic obstacles on the moving path of the end-effector and the behavioral constraints of the manipulator are not taken into account fully, since, for the spatial manipulators, they can bypass obstacles by its own joint rotation in 3D space. But for the planar manipulators, the dynamic obstacles cannot be bypassed because the joints of planar manipulators only rotate in a plane, which may result in the moving object not being grasped. Hence, considering these deficiencies of the planar manipulators in practice, a synthetic algorithm involving path prediction, path planning, and obstacles avoidance need to be further improved to track a moving object in a multiple-dynamic obstacles environment. Furthermore, in order to ensure the effectiveness of the synthetic algorithm, some developments on path prediction, path planning, and obstacles avoidance are also required, respectively.

In path prediction, the future positions of the object are always predicted first to achieve a moving object tracking. The common prediction methods contain Kalman filter [12, 13], learning algorithm [14], biomimetic approach [15], and polynomial fitting method [16]. Kalman filter can predict the current path based on the past information. Learning approach and biomimetic approach need a lot of offline training for many moving curves before prediction. Polynomial fitting method can predict many moving curves in the future by the polynomial calculation, and the error is small, but the motion paths are always considered as regular curves. Spline filter is an advanced method to smooth a large curve and it can ride the curve trend well [17], so Spline filter is raised to ride the trend of the moving paths for the first time in this paper. Then, polynomial fitting is introduced to predict the future moving paths of object and obstacles along their path trends.

On the basis of the predicted moving paths, the tracking path of the manipulator can be planned by search method [18], the artificial potential field method [19], neural networks [20, 21], ant colony algorithm [22], or C-space method [23]. But they all have some limitations. Since the computational amount of search method will increase sharply with the increase of space dimension, search method is difficult applied to plan paths in real-time. The artificial potential field method is suitable for dealing with dynamic obstacles, but it is easy to fall into local minimum point. Neural network method needs to be trained again when the environment changes. Ant colony algorithm has slow convergence speed and easily falls into local optimum. C-space method needs massive computation, but it is more intuitive and easier to plan a tracking path in a dynamic obstacles environment. So, C-space method is applied to plan a path for the end-effector to track the moving object in this paper. Besides, most of these methods are based on the hypothesis that the positions on the planned path could be reached by manipulators. However, in a multiobstacles environment, some positions on the planned path cannot be reached for the planar manipulator due to obstacles limiting the joint angles, which may result in the moving object not being grasped. That is, no criterion is set to judge whether the future position of the object along the planned path can be reached. Consequently, a feasibility criterion is defined to ensure that the path planned by C-space method is feasible for manipulator to grasp the object.

Although the tracking path is planned appropriately, the real-time obstacle avoidance for the end-effector and the manipulator arms, which is based on local obstacle avoidance approaches [24], still needs to be considered in the varying environment. Most of the local approaches aim at producing motions away from the obstacle for every point or each critical point on the manipulator when they are close to the obstacle in Cartesian space [25–28]. In the varying environment, the obstacles avoidance will be more complex. In [7], switching primary and secondary task and setting priorities are applied to avoid multiple obstacles. This paper will draw on this strategy and set the same priority for these obstacles to avoid the multidynamic obstacles in tracking the moving object at the same time.

Considering that the errors of predicting paths are small in a short time, the tracking path should be as short as possible and the tracking speed must be accelerated. In generally, the gain coefficient of the position error is constant [29]. To achieve fast tracking, a large gain coefficient is usually set, which results in large system gain. Besides, the joint driver overshoot and jitter will occur. Thus an adaptively adjusting method, in which gain coefficient varies with the change of the tracked object speed, is proposed to ease the process.

As previously described, some further studies still need to be done in moving path prediction, path planning, and the real-time obstacles avoidance. Meanwhile, these aspects must be synthesized effectively to track a moving object in a multiple-dynamic obstacles environment. Therefore, based on kinematically 6-DOF planar manipulator, this paper presents a synthetic algorithm to achieve a moving object tracking in a multiple-dynamic obstacles environment, which involves the moving path prediction, path planning, and the real-time obstacles avoidance. The algorithm applies the predicted moving paths of the object and obstacles to plan feasible paths, and an optimized path is selected among these feasible paths based on the shortest principle. A virtual controller is designed for the manipulator to adjust the tracking speed adaptively. Moreover, the local rotation coordinate method (LRCM), which is proposed by the authors, is used to avoid the obstacles that get close to the end-effector, and the null space of inverse kinematics is adapted to avoid obstacles in the vicinity of the manipulator arms. The supplementary material, which can demonstrate the proposed method, is available online (see Supplementary Material available online at https://doi.org/10.1155/2017/7310105).

This paper is organized as follows. Section 2 describes the real-time path tracking approaches by utilizing iterative method in the absence of obstacles. The strategies of tracking a moving object in the multiple-dynamic obstacles environment are developed in Section 3, involving moving path prediction, the optimized path planning, obstacles avoidance, and the synthetic object tracking algorithm. And the corresponding simulations are presented in Section 4. The conclusion is drawn in Section 5.

#### 2. Obstacles Free Case

##### 2.1. Based on the Common Method

As shown in Figure 1(a), the 3D model of 6-DOF planar manipulator is presented. The manipulator can only work in a plane with six rotary joints and the axes of joints are parallel to each other. And it is obvious to see that each joint is driven by an actuator directly. For a given task, the motion path of the end-effector is planned in Cartesian space at first. Then the rotation of each joint can be obtained by the inverse kinematic. Finally, according to the planned path, the movement of the manipulator is realized by the position control of actuators. In this paper, to facilitate the modeling and analysis of kinematics in Cartesian space, a simplified model is established based on the 3D model of 6-DOF planar manipulator as shown in Figure 1(b). Each thin solid line expresses an arm of the manipulator. Also, the line indicates the end-effector. The Cartesian coordinate is defined as the base coordinate system of the planar manipulator and the inverse kinematics of the 6-DOF planar manipulator iswhere is the velocity of end-effector in Cartesian space. is the position and attitude of end-effector, , is the attitude of end-effector, and . is the joint velocity of manipulator in joint space. is the joint angle; . is the pseudoinverse of Jacobian based on the damped least squares (DLS) method, , and . is the damping factor. . . ; . Jacobian is a desired matrix; that is, all parameters in are accurately identified. In application, always contains some errors, but the tasks can still be carried out normally. To prove this view, let be the Jacobian with some errors and the corresponding simulations are presented in Section 2.3.