This paper presents a synthetic algorithm for tracking a moving object in a multipledynamic 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 realtime path along the optimized path is planned for the manipulator to track the moving object in realtime. To improve the convergence rate of tracking, a virtual controller based on PD controller is designed to adaptively adjust the realtime 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 endeffector to avoid obstacles, respectively. Finally, the moving object in a multipledynamic obstacles environment is thus tracked via realtime 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 multipledynamic obstacles environment.
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 [
Typical researches on the manipulators with vision system aim at realtime tracking moving objects in the varying environment. Allen et al. introduce a control algorithm to predict ahead the trajectory of the object in realtime, and the tracking can be performed by kinematic transformation computation [
Nevertheless, to track a moving object in a multipledynamic obstacles environment, several technologies must be considered at the same time, containing moving path prediction, path planning, and realtime 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 multipledynamic 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 endeffector 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 multipledynamic 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 [
On the basis of the predicted moving paths, the tracking path of the manipulator can be planned by
Although the tracking path is planned appropriately, the realtime obstacle avoidance for the endeffector and the manipulator arms, which is based on local obstacle avoidance approaches [
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 [
As previously described, some further studies still need to be done in moving path prediction, path planning, and the realtime obstacles avoidance. Meanwhile, these aspects must be synthesized effectively to track a moving object in a multipledynamic obstacles environment. Therefore, based on kinematically 6DOF planar manipulator, this paper presents a synthetic algorithm to achieve a moving object tracking in a multipledynamic obstacles environment, which involves the moving path prediction, path planning, and the realtime 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 endeffector, 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
This paper is organized as follows. Section
As shown in Figure
Realtime tracking a moving object in absence of obstacles. (a) 3D model of 6DOF planar manipulator. (b) The simplified model of 6DOF planar manipulator.
In order to track a moving object in realtime, the velocity of endeffector,
In this paper, the iterative method is used to achieve the manipulator movement [
The control diagram tracking a moving object.
Based on the common method, the moving object can be tracked, but in order to increase the convergence rate, a large proportional coefficient is usually set and it is not flexible. So, a virtual controller, similar to PD controller, is designed to improve the convergence rate adaptively. Then
This simulation is to compare the common method with the proposed method. The object moves back and forth along a curve (
Parameters in the virtual controller.
Parameters 










Value  0.016  10^{−7}  2  0.05  0.02  300  100  0.2  0.6 
DH parameters of 6DOF manipulator.
Parameters  (mm)  Parameters  (mm)  Parameters  (rad) 


150 

140 

0.3 

150 

150 

0.3 

150 

160 

0.6 

150 

141 

0.5 

150 

155 

0.5 

150 

149 

0.8 
The comparison of the common method and the proposed method. (a) The position error between endeffector and object. (b) The attitudes
This paper assumes that the length
The changes of positions and attitude based on the proposed method in tracking a moving object. (a) The position error between endeffector and object. (b) The attitudes
In a multidynamic obstacles environment, avoiding the obstacles will limit the rotation range of the joint angles, which results in some positions within the workspace not being reached. So, before tracking the moving object, the grasped position of object should be predicted, and a reachable path should be planned for the manipulator. To complete the prediction and path planning, the initial motions of the object and obstacles are observed by camera or sensor at first. As shown in Figure
Observation, path prediction, and path planning.
This paper assumes that the object and the obstacles keep motions within the workspace of the manipulator, and their motions can be observed. Besides, the moving curves of the object and obstacles are smooth.
Consider that the moving paths observed by camera or sensor contain noises. Gaussian filter is always used to suppress the noises, but it suffers from edge effects due to the local weight average [
As shown in Figure
The angle
Similarly, the weights are fitted by a firstorder polynomial
Based on (
Then the following point
So, the convex polygons, which have influence on the paths, should be found out. Then, point
Based on (
The algorithm diagram of the optimized path.
Based on
The principle of obstacles avoidance on the path. (a) The overall layout. (b) The endeffector moves around the obstacle
Then the planned path
The realtime planned path
In the case that the obstacles are close to manipulator arms, the principle of avoiding obstacles is based on the critical points and there are five critical points on each arm as shown in Figure
On the basis of above analysis, an algorithm can be synthesized to track the moving object in a multidynamic obstacle environment, and the algorithm diagram is shown in Figure
The synthetic algorithm diagram of tracking a moving object in multipledynamic obstacles environment.
The first part of the simulation is to prove the exactness and the stability of the predicted path for the paths of the moving body in the future. Based on the initial 40 points, the future 20 points of three kind curves are predicted as shown in Figure
Comparison of the predicted path and the real moving path with noises for 20 points in the future. (a) Straight line:
According to (
The similarity degrees of the different motions for Figure
Similarity degree  Type  

Straight line  Circle curve  Combined curve  

0.9969  0.9891  0.8043 

0.9906  0.9814  0.8890 
The second part of the simulation is to verify the feasibility of LRCM. LRCM is used to avoid the obstacles that are close to the endeffector of manipulator. In Figures
Parameters for Figures
Parameters 







Value  80 mm  8 mm/s  63 mm/s  5  30 mm  1.0 × 10^{7} 
Parameters in the virtual controller.
Parameters 










Value  0.005  10^{−7}  1  10^{−3}  10^{−2}  300  100  0.02  0.02 
Avoiding the obstacle close to the endeffector by using LRCM in realtime. The initial joint angles
The third part of the simulation is to test the applicability of tracking the moving object with different speeds. As shown in Figure
Tracking the object with different moving speed.
The last part of the simulation is to validate the feasibility of the synthetic tracking algorithm proposed by the authors. Firstly, the simulation of tracking the moving object without observation and moving path prediction is presented as shown in Figures
The simulation of tracking the moving object in multipledynamic obstacles environment.
A synthetic algorithm, involving observation, moving path prediction, path planning, and realtime tracking, is proposed to track a moving object in a multidynamic obstacles environment for kinematically planar redundant manipulators. Spline filter combining with polynomial fitting is developed to predict the moving paths of the object and obstacles. The predicted moving paths and the defined feasibility criterion are used to plan paths of the endeffector in Cartesian space. Then the optimized path algorithm is raised for the manipulator to plan a tracking path. In tracking, the LRCM method is proposed for endeffector to avoid obstacles, and the null space of inverse kinematic is adopted for the manipulator arms to avoid obstacles. A virtual controller based on PD controller is designed to achieve the adaptive fast tracking. The moving object is thus tracked by updating the joint angles based on iterative method in realtime. Simulation results show that the predicting method of path is stable and accurate, the LRCM method is feasible for the endeffector to avoid obstacles, and the convergence rate of tracking can increase adaptively by using the virtual controller. Besides, the proposed synthetic algorithm is feasible to track a moving object in a multidynamic obstacle environment. Therefore, the synthetic algorithm is recommended by the authors.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China under Grants 61473102, 61503098, and 91648201 and supported by SelfPlanned Task of State Key Laboratory of Robotics and System (HIT), SKLRS201702A.