The modeling of an anthropomorphic robot arm

. This paper considers the anthropomorphic manipulator kinematics modeling problem. The considered anthropomorphic robot SAR-400 manipulator with five-fingered gripper has twelve degrees of freedom. In the paper the robot SAR-400 arm kinematic model and the simulation results are presented.


Introduction
From a mechanical point of view, like a human arm, the anthropomorphic robot arm is a kinematically redundant object [1]. Usually the anthropomorphic robot arm has seven degrees of freedom (DOF) from the shoulder to the wrist [1]. Kinematic redundancy leads to the abilities for robot manipulator to perform the end effector translation to a given position by an infinite number of trajectories. Such redundant manipulators have increased maneuverability and allow the manipulators to avoid falling into singular states and also can be effectively used in complex space-limiting areas [1][2][3][4].
There are two approaches are generally used for trajectory formation of such kinematically redundant manipulators. The one approach is based on finding the pseudoinverse Jacobi matrix and it can be used to determine the DOF velocities [5]. Thus, the required generalized coordinates increments can be determined by obtained velocities. The movements determining problem in redundant degrees of freedom allows manipulator to eliminate singular states, to avoid obstacles, and so on. Also, along with the requirement to move the end effector to an assigned position, additional goals can be reached. There are a number of other approaches, including those based on the fuzzy logic use to solve the inverse kinematics problem [6,7], but the gradient method is the most commonly used method for avoiding the constraints of mechanical joints when forming manipulator trajectory [1][2][3][4].
In this paper we consider the problem of anthropomorphic robot arm modeling. As a real research object, the left anthropomorphic robot SAR-400 [8] arm is considered. The robot arm modeling emulates human-like motions from the kinematics point of view. The paper is organized as follows. Section II describes the basic structure and features of the anthropomorphic robot SAR-400. The robot arm kinematics description is given in section III. Section IV illustrates forward and inverse kinematics modelling results of SAR-400 arm. Finally, section V summarizes the results and conclusions.

The anthropomorphic robot SAR-400
The robot SAR-400 [8] is a torso manipulator, which has an anthropomorphic structure and consists of a base frame, a body mounted on it, on which are mounted two anthropomorphic manipulators with five-fingered grippers, a head unit with a computer stereo vision system ( fig.1). This figure shows: 1 -head unit; 2 -compartment of stereo video cameras; 3rotary mechanism of the head unit; 4 -torso unit; 5,6,7,8 -rotational kinematic pairs of the manipulator; 9 -five-fingered gripper; 10 -rack for SAR-400. Each robot arm is a multilink manipulator with 12 degrees of freedom. The values of robot SAR-400 parameters are listed in the table 1.

The kinematics model of robot SAR-400 arm
The Fig. 2-a shows the coordinate systems and connection lines of the 12-DOF robot arm using the Denavite-Hartenberg convention that allows the construction of the forward kinematics function by composing the coordinate transformations into one homogeneous transformation matrix. The coordinate transformation description from (i-1)-th to i-th frames is given by the homogeneous transformation matrix [3,4] .  As far as it known [4] there are some situations when the Denavite-Hartenberg method do not allows us to construct joint frames effectively enough. For instance, this situation may appear when there is a necessity of describing hierarchical rigid body constructions by Denavite-Hartenberg method. In these cases, the resolution may be implemented by using auxiliary fixed frames that also can be described by Denavite-Hartenberg parameters. This ability is used into Matlab software in Robotics System Toolbox [9].
By using Matlab notation of Denavit-Hartenberg parameters the joint frames are formed by presented in Table 2 parameters. Here the index finger tip is chosen as an end-effector and is defined as a fixed joint. The little finger is omitted since it is synchronized to the ring finger. The Fig. 2-b shows the initial robot state defined into Matlab environment.
Since having defined a frame for each joint, the coordinate transformation describes the position and orientation of the end-effector with respect to the base frame is given by [3] { } ( ) , 1 7, 10 0 0 0 1 where θi is the joint variable, n  , o  and a  are the unit vectors of the attached to the endeffector frame, and p  is the position vector of the origin of this frame with respect to the origin of the reference frame ( fig. 2).   The paper presents the forward and inverse kinematics solutions for the robot SAR-400 anthropomorphic arm. The kinematics model was built by using Denavit-Hartenberg method and implemented into Matlab environment. The given modeling results shows the success of declared paper tasks. The complete robot SAR-400 kinematics model building and solution of the dynamics problems are the issues of the future work.
Studies were supported by the Ministry of Education and Science of the Russian Federation (project RFMEFI57818X0264)