Vladimir Matijevic

Control of Robots with Elastic Joints Interacting with Dynamic Environment

In this paper, the control of robots with elastic joints in contact with dynamic environment is considered. It is shown how control laws synthesized for the robots with rigid joints interacting with dynamic environment can also be used in the case of robots with elastic joints. The proposed control laws are based on a robot model interacting with dynamic environment, including the dynamics of actuators and the elasticity of joints. The proposed control laws possess two feedback loops: the outer, serving for “on-line” calculation of the motor shaft angle based on the position error or the contact force error, and the inner one, serving for performing stabilization around the calculated motor shaft angle. Simulation results which exhibit the application of the appropriate control laws are also presented.

Dynamics of robots with contact tasks

1. Robot Dynamics Problems, Research, and Results.- 2. Free Motion of a Rigid-Body Robot ARM.- 3. Rigid-Body Contact of a Robot with Its Environment.- 4. Soft and Elastodynamic Contacts.- 5. Robot Interacting with Complex Dynamic Environment.- 6. Dynamics of Multi-ARM Cooperative Robots with Elastic Contacts.- 7. New Trends in Contact Tasks.- 8. Appendix 1.- 9. Appendix 2.

Internal Redundancy – the Way to Improve Robot Dynamics and Control Performances

The research follows the concept of variable geometry. The concept was originally introduced for general mechanical system in order to improve its dynamic behaviour [14]. Here, we apply the concept to robots. It can be shown that enhancement of robot dynamic performances is achieved. In this paper variation of geometry is considered equally as the motion in robot joints. Thus, a new set of degrees of freedom is introduced. This leads to redundancy – different internal motions are possible for the given external motion of the end-effector. However, there is an important difference from the usual notion of redundancy. Here, the additional joints do not influence the external motion and accordingly cannot improve the end-effector ability for maneuvering. For this reason the new notion is defined the internal redundancy.Although variation of geometry is treated equally with the motion in robot joints, there is still a difference in the aim of these new degrees of freedom. They should contribute to overcoming the limits of robot actuators, achieving better static compensation, etc. One might say that internal redundancy improves the robot dynamic capabilities. In this paper the mathematical formulation of kinematics and dynamics of robots with internal redundancy is carried out. A case study is presented in order to support the main idea.

Dynamics of Contact Tasks in Robotics. Part II—Case Study in Dynamics of Contact Motion

The paper discusses some practical problems of contact dynamics. The general model derived in Part 1 of the paper is applied to a particular system. The following cases are studied: robot in contact with a transport cart, task of writing over a surface with friction, and influence of transmission elasticity on contact behaviour. In all cases, elastodynamic effects in a contact zone are included in the model. The problem of controlling motion and force is discussed and the simulation results are presented.

Contribution to the study of dynamics and dynamic control of robots interacting with dynamic environment

The paper discusses some practical problems of contact dynamics. Modelling the dynamics of contact tasks is carried out in a completely general way. Two dynamic systems, active robot system and passive environment system are brought into contact and the relevant dynamics are analyzed. The effects are: rigid-body contact force, elastodynamics in contact zone, friction in contact points, etc. Simultaneous stabilization of contact force and position is obtained using New Dynamic Position/Force Control. The general model is then applied to some more concrete problems and the simulation results are presented.

Robot Dynamics — Problems, Research, and Results

We start our discussion on robot dynamics from the standpoint that successful design and control of any system requires qualified knowledge of its behavior. This is certain, but we should explain what is meant by “qualified knowledge”. Let us consider a robot as an example of a technical system. Qualified knowledge of its behavior may, but need not, include the mathematical model of its dynamics. In the earlier phases of robotics development, design was not based on exact calculations of robot’s dynamics but followed the experience gained in machine design. The control did not take account of many dynamic effects. Large approximations were made to reduce the problem to the well-known theory of automatic control. The undeveloped robot theory could not support a more exact approach. For a long time, the practice of robotics (design, manufacturing, and implementation) was growing independently of the theory which was too academic. However, this did not prevent the manufacturers from constructing many efficient robots.

Free Motion of a Rigid-Body Robot Arm

This chapter considers the problems of dynamics assuming that robot links are infinitely rigid. The discussion starts with relevant ideas from the theory of mechanisms (kinematic pairs and chains, degrees of freedom, etc.) and then defines the parameters that describe the robot link geometry. Kinematics and dynamics concern free motion of the robot arm. Dynamic model of the robot chain is expanded by introducing the actuator dynamics and elastodynamics of the transmission system. Finally, some issues of control are elaborated.

Robot Interacting with Complex Dynamic Environment

The discussion about contact systems conducted in the previous chapters was based on one common idea — analysis of the robot with the constraints imposed to the motion of its end-effector. The constraints represented the robot environment. The discussion started with geometric constraints (Chapter 3). As a suitable example, the surface-type constraint was elaborated in detail. After that, elasticity in the contact zone was introduced: first, the deformation through stiffness and damping, and then elastodynamics through lumped masses. Although the problems discussed were rather complex, they could be simply described as “the robot’s end-effector in contact with the support”. It should be pointed out that many practical problems may be treated in this way (writing, assembly tasks, deburring, and other process operations, etc.). The restriction was that the object processed was placed on an immobile support or, if mobile, it moved according to a prescribed law that could not be affected by the robot action.

Rigid-Body Contact of a Robot with Its Environment

In this chapter we discuss the contact tasks in which the robot environment is considered as a geometric constraint imposed to the motion of the end-effector. The first general approach to this problem was presented in [1].

Dynamics of Multi-ARM Cooperative Robots with Elastic Contacts

In this Chapter, the procedure of modeling and the complete general form mathematical model of manipulators with six degrees of freedom (DOF) in cooperative work are presented, together with the solution of the indefiniteness problem with respect to force distribution. The obtained model is presented in several convenient forms. For the first time, a system of active spatial six-DOF mechanisms elastically interconnected with the object (dynamic environment) is modeled. The reason for the emergence of the indefiniteness problem with respect to force is explained and the procedure for solving this problem is given. Unlike the approaches given in the available literature, the indefiniteness problem with respect to force is solved in accordance with physical phenomena.