Manja V. Kircanski

A dynamic approach to nominal trajectory synthesis for redundant manipulators

The solution to the inverse manipulation problem for redundant manipulators has mostly been considered from a geometric-kinematic standpoint. A procedure for the inverse problem solution using the dynamic model of the manipulator and its actuators is developed. Nominal trajectories in the space of joint coordinates are generated so as to be optimal with respect to total energy consumption of the actuators (hydraulic or electric). The treatment of constraints on joint coordinates and rates is also involved in the procedure. The algorithm is illustrated by two industrial robots.

Kinematics and trajectory synthesis of manipulation robots

1 Kinematic Equations.- 1.1. Introduction.- 1.2. Definitions.- 1.3. Manipulator hand position.- 1.3.1. Rodrigues formula approach.- 1.3.2. Homogeneous transformations.- 1.3.3. Spherical coordinates.- 1.3.4. Cylindrical coordinates.- 1.4. Manipulator hand orientation.- 1.4.1. Euler angles.- 1.4.2. Euler parameters.- 1.5. Manipulator hand velocities.- 1.5.1. Recursive and nonrecursive relations for linear and angular velocities.- 1.5.2. The Jacobian matrices.- 1.6. Summary.- 2 Computer-aided Generation of Kinematic Equations in Symbolic Form.- 2.1. Introduction.- 2.2. Symbolic kinematic equations.- 2.2.1. Backward and forward recursive relations.- 2.2.2. Kinematic equations for the UMS-3B manipulator.- 2.2.3. Backward recursive symbolic relations.- 2.2.4. Forward recursive symbolic relations.- 2.2.5. Treatment of revolute joints with parallel joints axes.- 2.3. The Jacobian matrix with respect to the hand coordinate frame.- 2.3.1. The Jacobian for the UMS-3B manipulator.- 2.3.2. Recursive symbolic relations for the Jacobian with respect to the hand coordinate frame.- 2.3.3. The Jacobian columns corresponding to parallel joints.- 2.4. The Jacobian matrix with respect to the base coordinate frame.- 2.4.1. The Jacobian for the UMS-3B manipulator.- 2.4.2. Recursive symbolic relations for the Jacobian with respect to the base coordinate frame.- 2.4.3. The Jacobian columns corresponding to parallel joints.- 2.5. Program implementation, numerical aspects and examples.- 2.5.1. Block-diagram of the program for the symbolic model generation.- 2.5.2. Examples.- 2.5.3. Numerical aspects.- 2.6. Summary.- Appendix I Direct Kinematic Problem for the Arthropoid Manipulator.- Appendix II The Jacobian with Respect to the Hand Coordinate Frame for the Arthropoid Manipulator.- Appendix III The Jacobion with Respect to the Base Coordinate Frame for the Arthropoid Manipulator.- 3 Inverse Kinematic Problem.- 3.1. Introduction.- 3.2. Analytical solutions.- 3.3. Numerical solutions.- 3.4. Summary.- 4 Kinematic Approach to Motion Generation.- 4.1. Introduction.- 4.2. Manipulation task.- 4.3. Trajectory planning.- 4.4. Motion between positions.- 4.4.1. Joint-interpolated motion.- 4.4.2. External coordinates motion.- 4.5. Procedurally defined motion.- 4.6. Summary.- 5 Dynamic Approach to Motion Generation.- 5.1. Introduction.- 5.2. Manipulation system dynamic model.- 5.3. An overview of methods for dynamic motion synthesis.- 5.4. Determination of the energy optimal velocity distribution using dynamic programming.- 5.5. Quasioptimal nominal trajectory synthesis using decentralized system model.- 5.6. Summary.- 6 Motion Generation for Redundant Manipulators.- 6.1. Introduction.- 6.2. Kinematic methods for redundant manipulator motion generation.- 6.3. Energy optimal motion synthesis.- 6.4. Obstacle avoidance using redundant manipulators.- 6.5. An algorithm for redundant manipulator motion synthesis in the presence of obstacles.- 6.6. Summary.- References.

A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form

This paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form. The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.

Resolved-rate and resolved-acceleration-based robot control in the presence of actuators' constraints

Experimental evaluation of various task-space control algorithms shows that significant deviations from desired trajectories may occur, especially at higher speeds, or in the vicinity of singularities. The experiments on a modular reconfigurable robotic setup confirmed this conclusion: the lateral deviations may range up to several centimeters from the closest point on the desired trajectory. The main reason is that the control output often reaches the saturation value of an actuator. The lateral error is also found very dangerous in obstacle cluttered environments due to possible damage of the manipulator arm while hitting an obstacle at high speed. This paper is devoted to solve this problem. Widely used task space control algorithms such as the resolved-rate and the resolved-acceleration algorithms are modified by introducing monitoring on the control output, and, accordingly, modifying the commanded control signal so that the end-effector is prevented from leaving the programmed path. As a consequence, the manipulator tip may slowdown along the path due to limited actuator power, but it will be accelerated after that to reach the desired position as soon as possible. The algorithms also take into account the presence of singularities to avoid uncontrollable excursions of the manipulator tip. Hundreds of experiments have been carried out to confirm the concept. Some of those with a desired trajectory reaching both the regular and the singular region of the workspace are provided to illustrate the method.

An experimental study of resolved acceleration control in singularities: damped least-squares approach

In this paper the application of the damped least-squares method to the resolved-acceleration control is experimentally examined on a 2-DOF planar manipulator In order to decrease the position error introduced by the damping, only small singular values are damped. The symbolical expressions of the singular value decomposition of the Jacobian matrix were utilized in order to decrease the computational burden. Position error along the work-space boundary was only 15% greater than along the trajectories inside the reachable workspace.<<ETX>>

Inverse kinematic problem near singularities for simple manipulators: symbolical damped least-squares solution

The application of damped least-squares in solving the inverse kinematic problem near singularities requires numerically expensive singular value decomposition (SVD) of the Jacobian matrix and introduces some position error. Here the damped least-squares solution is obtained by dividing the Jacobian matrix into several submatrices of the order 1*1 or 2*2 and deriving a symbolic SVD for these submatrices. This is possible for simple manipulators where the inverse Jacobian can be obtained in analytical form. The SVD for the trivial 1*1 submatrices are also trivial, while for 2*2 matrices it can be easily derived in symbolic form. Simulations carried out at the kinematic control level for the Stanford manipulator and the PUMA-600 robot show that very good tracking of the specified trajectories may be achieved. Position error outside the trajectory is reduced to minimum, while the joint velocities are limited.<<ETX>>

Computation of customized symbolic robot models on peripheral array processors

The authors address the problem of the optimal evaluation of robot inverse dynamics on array processors. The inverse dynamics models used are the symbolic customized models with near-minimum numerical complexity, which are computer-generated given the robot arm parameters. Such models represent the input for a proposed scheduling algorithm that distributes the computation of the model over several multipliers and adders. The scheduling algorithm is automatic and minimizes the number of microcycles. The algorithm was tested on several standard robots, and processor efficiency up to 84% was achieved. Experimental results on a 30 MFLOPS array processor showed that the inverse dynamics of a three-link PUMA-like robot requires 25.5 mu s. For a six-link robot, the computation of the inverse dynamics and the control law takes about 100 mu s on this processor. Thus, the control of high-speed robots could be achieved by attaching low-cost array processors (10 MFLOPS) to the control processor of the robot controller.<<ETX>>

One method for simplified manipulator model construction and its application in quazioptimal trajectory synthesis

Abstract In this paper a computer method for automatic setting of simplified dynamic models of open, active mechanisms is proposed. The algorithm is based on the well-known method of general theorems of mechanics for automatic setting of the complete model of these mechanisms. The simplified model takes into account inertial and gravitational terms, while the influence of Coriolis and centrifugal forces is neglected. The accuracy of the simplified model is examined on several examples. The simplified model is also utilized for optimal manipulator trajectory synthesis. It is shown that the use of the simplified model considerably reduces computational time, and at the same time ensures the same optimization results as the use of the complete dynamic model.

Multiprocessor control system for industrial robots

Abstract This paper describes an advanced robot control system based on the three parallel processor boards. The controller has been designed as a general-purpose robot control system dedicated to controlling industrial robots with up to six degrees of freedom. The controller is based on a disk-oriented real-time operating system. The entire set of robot parameters can be monitored and changed by the user on-line. Source files, compilers, linkers and various utilities are provided as well. The main software layers include robot program interpreter, manipulator control facility, robot kinematics, dynamic feed-forward compensation, and digital servos. Basis, hand and joint coordinates are supported. Point-to-point and continuous path motions are provided. Digital and analog IO modules are included for synchronization with an environment. An acquisition system for monitoring and graphical presentation of robot coordinates, velocities and IO signals is provided. The paper ends with some experimental results for a six-degree of freedom robot.

Symbolic modeling in robotics: Genesis, applicaton, and future prospects

This survey article gives an overview of software packages for generating numerically efficient manipulator models in symbolic form, i.e. as computer programs written in a high-level language such as C or FORTRAN. We chronicle the history of computational robot dynamics and, to some extent, multibody systems dynamics. We survey several mechanical computer-aided engineering software packages because they have charted the course for symbolic robot modeling software. The attractive features of various programs regarding areas of application (vehicles, robots, satellites, etc.) and design possibilities (kinematic and dynamic analysis, modal analysis, optimization of mechanical design, numerical efficiency of generated symbolic models, etc.) are emphasized. Finally, as an example, we present the SYM program package in more detail and point out the new strategic area of robotics which has emerged during the last two years: computer-aided generation of control laws.