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Camera robot is an important tool for realizing and reproducing complex camera motion path in modern special film effects. This paper proposed an inverse kinematics optimization algorithm for PRRPR-S redundant degrees of freedom (DoF) camera robot. This paper analyzed the motion characteristics, in Genetic Mix (GM) method, from the idea of movement boundary composed of part robot axis. Then proposed Simplify Mix (SM) method which can stably converge to the global optimal solution in a shorter time.

The PRRPR-S robot, referred to as camera robot, is an important tool of reproducing camera movement for multilayer composite film effects and realizing complex camera motion path. It is an important interactive node in film virtual manufacturing [

The algebraic equation form of redundancy serial robot inverse kinematics on velocity level is linear style [

Masayuki et al. [

The camera robot needs to get the position and attitude of the end-effector exactly in practice. And it has 8 joints, corresponding to high dimension of solution space, in other words, low effective solution proportion space. By using GA method based on forward kinematics equations, it is difficult to find valid solutions and attach other optimization goals. In addition, the randomness of the initial population makes the existence probability of the effective individuals very low, and the algorithm convergence effect is poor. Taking the axes of

The camera robot is shown in Figure

Camera robot.

Schematic diagram of camera robot mechanism.

The kinematic link parameters are shown in Table

Robot link parameters.

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The DH matrices of camera robot are as follows:

The values of Table

Temporarily assume that the end-effector of the camera robot can get any posture through the wrist. As the robot moving in the bottom linear rail, the reachable space of

Workspace boundary of the camera robot.

Considering that the industrial 6-DoF robot has mature algorithm of inverse kinematic solution, the bottom linear axis (

For clarity, declare the axis physical motion range as physical constraint and geometric constraint as theoretical constraint. The intersection of two constraints is the range which contains effective solution, called comprehensive constraint.

When using GA method with physical constraints of

Note the following:

As for the rail can be extended to any length, the physical constraint of

At different heights, there are specific theoretical maximum

Theoretical max/min

Ask

Reaching different

If

Thus,

When the camera robot reaches

Reaching

When the camera robot reaches

Reaching

According to

After arbitrarily determining

The inclusion relation of factor sets is

Select an arbitrary

Given the target posture,

The physical limit state of

Take

According to the geometric principal,

The general case when

Before interpartition analysis, discuss the function:

After determining

The blue sector (filled with upper right oblique line) is

According to the following principles, get

Effective

With

As the standard examples, Figures

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When

And when

When

When

And when

There is

In summary, on the basis of the boundary of the camera robot workspace,

The optimization goal is to improve the motion stability of the end-effector; this paper sets the motor shaft to move as little as possible with the higher load inertia. The optimization objective function

According to the camera robot motion characteristics,

In the experiment, it is found that the optimal solution of GM did not change or change little in the process of iterative computation. That is, the analysis of camera robot motion characteristics with average initial population distribution greatly weakened the global optimization effect of GA in GM. So it is desirable to solve in a shorter time by motion characteristics with pattern search. This paper proposed SM method. To verify the effect of it, set the experiment.

The robot is in the initial standard zero state. 4 to 8 meters in the positive direction of the rail, set 45 target postures evenly. Specifically, five planes are set in the space, and 9 target postures are distributed in each plane, as shown in Figure

Target postures in workspace.

Assume that both

Set the physical constraints of each axis as

Define

Take the experiment as follows.

Select 20 values in

Calculate the optimal solutions by GM and SM methods, respectively. The result is shown in Figure

Compared result of two methods.

For 45 target postures, GM costs 6328.32 s and SM costs 3410.07 s. There is only one posture with big distance appearing on the 30th posture, where the ratio of two values of optimal objective function is 12%, and GM method gets a better solution. The robot states are shown in Figure

Maximum deviation of two methods.

In summary, SM method is more convenient in practical application than GM.

In this paper, the motion characteristics analysis of PRRPR-S robot is discussed; GM method overcomes the defects of dual redundancy sequence and stochastic of GA. The experiment in Section

Even though the kinematic solution method is for PRRPR-S robot, by using the idea of subworkspace and motion path, combining with pattern search, any other type of redundant robot can get the inverse kinematic solution. This is the significance of SM method.

The author declares that there are no conflicts of interest related to this paper.