论文总字数：13107字

Trajectory planning of anthropomorphic arm

Abstract

In this paper, an algorithm for the direction control of endpoint position error caused by disturbance is proposed. With this in mind the effect of the disturbance on the position of the endpoint is maximized in the direction of the singular vector corresponding to the maximum singular value.Therefore, if we can control the direction of the singular vector, we can control the direction of the endpoint position error guided by the disturbance. The algorithm is applied to the hit motion of the manipulator, and the control algorithm and effect of the position error direction are presented.

Trajectory planning of anthropomorphic arm

1. Introduction

In general, we cannot get the nominal model of real robot system, because real robot system contains various uncertainties. One uncertainty is noise and interference, which are excluded from the nominal model.For example, sensor noise and angular velocity quantization errors act as disturbances on the robot. In order to suppress disturbances, many scholars focus their research on the design and trajectory planning of robust controllers [2] and [7]. The design and trajectory planning of the controller is very complicated.At the same time, our concept is to effectively use the dynamics of the robot to complete the task of robustness, even if the controller is very simple. Therefore, we focus on motion planning rather than controller design and trajectory planning.If the robust trajectory can be obtained independently of the control input, the controller can be simplified. In order to reduce the influence of disturbance on the task, we use the dynamic characteristics of the robot to plan the motion proactively. As far as we know, although the motion planning of [1], [9], [8] and other mechanical arms has been proposed, these schemes do not involve the problem of disturbance suppression.The results show that this method can effectively reduce the position error of the final point. On the other hand, this paper focuses on the direction of endpoint position error. In some tasks, the direction in which the position error is generated is more important than its size. One of these tasks is the strike motion of the robotic arm, as shown in figure 1. If the endpoint is disturbed and deviates vertically to the desired trajectory, the robot cannot hit the target, as shown in figure 1(a). If the direction of the position error can be controlled to be tangent to the desired trajectory, as shown in the figure. 1(b),Even with interference, the manipulator can hit the target. For hitting motion, there is no need to force the manipulator to reduce the size of position error. As long as the direction of position error can be controlled, the robustness of batting motion against disturbance can be improved. Therefore, this paper only deals with the generating direction of endpoint position error, and proposes a technology to control the generating direction to the tangential direction of the target path.

Fig. 1. Application examples of the control of direction of the end-point

position error caused by disturbance

In the traditional motion planning of industrial robots and redundant robots, the task is usually simple and fixed, and the planning is realized by optimizing predetermined performance indexes such as dexterity, joint limitation, torque limitation and obstacle avoidanceWith the gradual maturity of industrial manipulator technology, production efficiency is greatly improved, and the demand for robots in factories is also gradually reduced. Therefore, the research focus in the field of robotics has shifted from industrial robots [7] to service robots, and humanoid robots play a very important role in the field of service robots. Due to the various requirements faced by humanoid robots, the humanoid arm must be able to handle more complex task-level operations.At the same time, the anthropomorphic arm hopes to move in a familiar way to help robots and humans coexist [8]. Traditional planning methods cannot be used for the above requirements. They can only plan a trajectory to achieve the simple task of mimicking a human arm functionally and improve performance during movement. However, they cannotControl the motion process in the attitude aspect.The problem of anthropomorphic arm movement planning has been studied by many scholars [9]-[11]. There are two schools of thought: the empirical statistical model school and the inverse kinematics solution school. The former first collects human measurement data from human experiments, and then USES regression model and other model tools to conduct statistical analysis on the data, forming attitude prediction model. The weakness of this school of thought is its lack of universality. In this way, it would be impractical to have to carry out a large number of experiments involving human bodies for each specific task.The latter usually USES biomechanics and kinematics as planning tools to solve joint trajectory by optimizing performance indexes and satisfying constraints. The deficiency of this method is the lack of experimental support, and many indicators are constructed by guessing.In recent years, more and more neurophysiological studies have shown that there are motion protectors in the movement of human arms [13]-[16].In the process of continuously completing a large number of tasks, human beings have formed a series of operational experience, which has evolved into a set of fixed motion mode, i.e movement primitives. In this way, one can easily assemble different motion primitives to perform difficult tasks such as building blocks, regardless of how each joint moves.Undoubtedly, this method provides a new way of thinking for motion planning, which is faced with a variety of business needs. By introducing the concept of anthropomorphic arm motion primitive, a new method of motion planning for complex tasks is proposed.

2 design and trajectory planning of an anthropomorphic robot arm

Our research goal is to build a service robot similar to human beings to support people's daily life. The main part of the robot used to process objects is its arm structure. Our FZI arm design and trajectory planning is based on the observation of the range of motion of the human arm. The average range of motion of the arm on the shoulder in healthy people is about 160 degrees in horizontal bending, 240 degrees in forward bending and over stretching, and 160 degrees in medial and lateral rotation. The normal range of motion of the elbow is 150 degrees. Wrist joint in radial/ulnar deviation mode is 70 degrees, bending/stretching about 170 degrees, the maximum range of motion is 1.5 meters. The wrist rotates 270 degrees. In addition, the overall physical structure, size, shape and kinematics of Fzi arm should be as close as possible to human arm. The so-called anthropomorphic mechanism is developed in industrial robotics. It must provide good dynamic performance, usually very simple. In mechanical sense, it is only a rough copy of human arm.

From the mechanical point of view the human arm mechanism particularly the shoulder joints is the one of the most complex parts of the human body [10], [8]. Previous studies related to the modeling of the human arm kinematics [8] [15] show that the complexity of the shoulder joints (the gleno-humeral joint and the shoulder girdle which includes the clavicle and scapula and their articulations is critical. According to [3] the human arm mechanism is composed of seven degrees of freedom three in the shoulder two at the elbow and two at the wrist. It can be modelled by a first order approximation as a mechanical manipulator consisting of a series of links connected by one degree of freedom (DOF) rotational joints each specifying a selective motion Figure1 shows the simplified kinematics model of the human arm. This kinematics mo del is the base for the design and trajectory planning and construction of the FZI arm.

Because of the high complexity of the mechanic of an anthropomorphic hand and to fulfill in general the requirement of a low-cost arm the hand will be realized as a quite simple gripper.

Figure 1 Simplified kinematics model of the human arm

2.1 The upp er arm design and trajectory planning

For a first rapid construction of the new robot arm we used as upper arm design and trajectory planning the leg construction of our six-legged machine LAURON I I [5] It has two degree of freedom in the shoulder and additional one in its elbow . In each of the three joints the power transmission is done via planet gears and ropes. The torque of the joint is ab out 5Nm, that of the joint 33Nm and the joint 9.3Nm. This design and trajectory planning concept was used because it allows a large range of motion adequate torques and joint angle velo cities? This first upper arm construction can be seen in figure6. For more information see [33]

Since this construction represents only a very rough approximation of the human arm, we decide to develop a new anthropmorphic upp er arm as presented in figure 1. This work is still under Development.

2.2 The forearm construction

The aim of the forearm design and trajectory planning was to develop a leight-weight arm with a slim and compact type of construction. Therefore first different concepts for the positioning of the four motors are examined. In fig2 the optimal arrangement of the motors are shown. This space saving design and trajectory planning has the advantage that moment of inertia according to the longitudinal axis of the forearm is very low. Additionally, the center of gravity is near the elbow. This principle reduces the weight limit of upper arm.

Figure 2 The concept of the positioning of the motors. This design and trajectory planning allows a space saving arrangement of the motors.

The wrist construction allows a power transmission between forearm and gripper. It has 2 DOF each. Both axis of motion are pointed intersect in the universal joint (see fig3) The drives for the wrist motion is a combination of ropes and screw ball units. The screw ball units are selected because they generate large force with effectiveness over. The forces are transmitted via ropes and rolls towards the wrist? The effectiveness of the ropes is more than 90%. As result huge torques for the wrist can be generated with high effectiveness.In fig4 the drive concept for the wrist is shown.

Figure 3: The range of motion of the wrist

2.3 The gripper

The gripper design and trajectory planning is shown in fig5. The gripper consists of four small sticks? which are moved in parallel. The power transmission is also done with the help of ropes, effectiveness more than 95%. The ropes are winded around special rolls in a way so that the drive?shaft can fixed in radial direction. This allows a very space?saving and cheap construction. All components of the FZI arm are presented in fig6.

Figure 4: Drive concept of the wrist? Two screw ball gears are used for the control of the two axis of the wrist. The power transmission is done via ropes.

Figure 5 Construction of the gripper driven by ropes.

Figure 6 The FZI arm It has 3DOF in the upper arm, DOF in the forearm and 2 DOF in the gripper.

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