F. Karray

On the control of a class of flexible manipulators using feedback linearization approach

Abstract The paper studies nonlinear dynamics and control of the Space Station based mobile, flexible, two-link manipulators accounting for elastic character of the joints. The governing highly nonlinear, nonautonomous and coupled equations of motion are described first followed by the modal discretization procedure. A parametric response study suggests situations with unacceptable levels of deflections and accelerations for certain proposed missions, as well as station libration and payload positioning errors. An inverse control technique is suggested to achieve high tracking accuracy of the MSS in presence of maneuver induced as well as other external and internal disturbances. The control strategy is so designed as to regulate the libration of the Space Station and to insure joints tracking of prescribed trajectories, while limiting the effect of the structural vibration during large slewing maneuvers of the MSS. Two different control schemes, both based on the feedback linearization technique, are developed and their relative merit assessed.

On the nonlinear dynamics and control of flexible orbiting manipulators

The paper studies nonlinear dynamics and control of a class of space station based mobile flexible two-link manipulators, normally referred to as the Mobile Servicing System (MSS).The paper studies nonlinear dynamics and control of a class of space station based mobile flexible two-link manipulators, normally referred to as the Mobile Servicing System (MSS).The governing nonlinear, nonautonomous and coupled equations of motion are described first followed by the modal discretizations procedure. A parametric response study suggests situations with unacceptable levels of deflections and accelerations for certain proposed missions, as well as station libration and payload positioning errors.An inverse control technique is proposed to achieve high tracking accuracy of the MSS in presence of maneuver induced disturbances. The control strategy is so designed as to regulate the libration of the Space Station as well as to insure joints tracking of prescribed trajectories, while limiting the effect of the structural vibration during large slewing maneuvres of the MSS. Two different control schemes, both based on the feedback linearization technique, are developed and their relative merit assessed.

A composite control scheme for joint tracking and active vibration suppression of mobile flexible manipulator systems

Abstract A composite control scheme for dealing with the settling and joint tracking behavior with active vibration suppression of a relatively general model of an orbiting platform supporting a multi-link flexible manipulator system is proposed. To begin with, the dynamics of the system is derived. A non-linear control procedure for dealing with the non-linear character and mode coupling of the system, is then proposed. The main objective here is to achieve a high tracking performance at the manipulator joints, and actively suppress vibrations of the flexible arms caused by slewing and translational maneuvers. Based on a composite control scheme combining the input-output feedback linearization technique with the piezoelectric active vibration suppression, the procedure allows for a high performance of the manipulator both in joint as well as in tip trajectory tracking. Numerical simulations are then carried out for the purposes of validating the analytical dynamical model and the control synthesis thus developed, and recommendations for further analysis are proposed.

A general formulation for the nonlinear dynamics and control of orbiting flexible structures

A relatively general Lagrangian formulation for studying the dynamics of a large class of spacecraft characterized by interconnected flexible members forming a tree topology, is presented. Methodology and development of the computer code suitable for parametric dynamical study and control are briefly outlined. Versatility of the general formulation is demonstrated through dynamics studies of the Permanently Manned Configuration (PMC) of the proposed Space Station Freedom and the slewing dynamics and control of the two-link Mobile Servicing System (MSS) aboard Freedom. The PMC study indicates the effect of flexibility cannot be overlooked. Even a small disturbance on the main or stinger can result in unacceptable magnitudes of velocity and acceleration. The MSS study compares the system response subjected to the InPlane (IP) and Out-of-Plane (OP) maneuvers. Results indicate that, without control, the OP maneuver excites large yaw motion of the Space Station. Consequently, the OP maneuver has a large pointing error. Nonlinear control, based on the Feedback Linearization Technique, appears promising. By controlling the librational motion of the station, the performance of the OP maneuver improves significantly.

Path planning with obstacle avoidance as applied to a class of space based flexible manipulators

Abstract The present study is a natural extension to the earlier work carried out by the authors in the area of nonlinear control of flexible structures using the Feedback Linearization Technique (FLT). This procedure accounts for the complete nonlinear dynamics of the system. It develops a rather innovative approach to path planning, for a 2-link flexible manipulator, with a specified target and several arbitrarily positioned obstacles. It is important to point out that the presence of link vibrations makes the problem at least an order of magnitude more complicated rendering the conventional algorithms developed for rigid systems virtually of little use. The problem involves generation of regions (contours) representing spheres of influence around the finite size obstacles, with various degrees of permissible penetrations during path planning to the target. To begin with, equations of motion of an orbiting flexible manipulator, undergoing planar slewing maneuvers, are obtained accounting for a shift in the center of mass during maneuvers. Next, a composite control procedure, involving the FLT together with active vibration suppression using piezo-electric actuators, is developed which promises high degree of tracking accuracy. Depending on the performance requirement of the mission, penalty functions are assigned for a given performance index pertaining to the flexible dynamics of the systems. This permits global improvement of the manipulator operation. Finally, effectiveness of the collision avoidance scheme is illustrated through several examples of increasing complexities.

Slewing dynamics and control of the Space Station-based mobile servicing system☆

Abstract A relatively general Lagrangian formulation for studying the non-linear dynamics and control of spacecraft with interconnected flexible members in a tree-type topology is developed. Versatility of the formulation is illustrated through a dynamical study of the Space Station-based two-link mobile servicing system (MSS). The performance of the MSS undergoing inplane and out-of-plane slewing maneuvers is compared. Results indicate that, in absence of control, the maneuvers induce undesirable librational motion of the Space Station as well as vibration of the links. Non-linear control based on the feedback linearization technique (FLT), appears promising. Quasi-closed loop control (QCLC), a variation of the FLT, is applied to control the libration of the Space Station. Once the attitude of the Space Station is controlled, the performance of the MSS improves significantly. For a 5-min maneuver of the MSS, the maximum control torque required is only 34.5 Nm.

Non-linear decoupling control of a flexible space platform☆

Abstract A decoupling control procedure for settling performance of a space platform in the presence of induced disturbances is described. The control strategy is so designed as to decouple and regulate the librational dynamics of the flexible platform when the platform-based mobile robotic manipulator is undergoing translational and slewing maneuvers. The equations of motion governing the system dynamics are first derived based on a relatively general model applicable to a large class of systems characterized by interconnected flexible and/or rigid bodies forming a chain-type topology. The Lagrangian formulation, accounting for an arbitrary number of Eulerian beam-type members, is well suited for a parametric study to identify critical combinations of systems parameters leading to unacceptable response. Preliminary results suggest an unstable behavior of the uncontrolled system in the presence of the manipulator maneuvers. Effectiveness of the controller is illustrated through an example involving maneuvers, both in and out of the orbital plane, showing excellent settling performance of the librational degrees of freedom.

Nonlinear dynamics and control of orbiting structures: an approach with applications

A relatively general Lagrangian formulation for studying the nonlinear dynamics of spacecraft with interconnected flexible members in a tree-type topology is developed. The governing equations of motion are coupled, nonlinear, and nonautonomous; hence, nonlinear control, based on the Feedback Linearization Technique (FLT), is incorporated. Versatility of the formulation is illustrated through dynamical studies of the multipurpose telecommunications satellite, Indian Satellite II(INSAT-II) and Space Station based two-link Mobile Servicing System (MSS). The uncontrolled dynamics of the INSAT-II shows that the flexible spacecraft to be in an inherently unstable equilibrium orientation. Control, based on the FLT, is then applied to restore the desired attitude of the spacecraft. The performance of the MSS undergoing inplane and out-of-plane slewing maneuvers is compared. Results indicate that, in absence of control, the maneuvers induce vibration of the links as well as undesirable librational motion of the Space Station. Control is next applied to the Space Station. Once the altitude of the Space Station is controlled, the performance of the MSS improves significantly.<<ETX>>

Nonlinear dynamics and control of INSAT-II: application of a general formulation

The paper presents a general Lagrangian formulation capable of studying the nonlinear dynamics and control of spacecraft with interconnected members in a tree-type topology. The nonlinear control, based on the feedback linearization technique (FLT) is adopted. The simplicity of the control algorithm and its applicability to both rigid and flexible spacecraft make the technique quite attractive. Application of the formulation is illustrated using a spacecraft of contemporary interest, INdian SATellite-II (INSAT-II), a next generation of multipurpose communications spacecraft launched in August 1992. The uncontrolled dynamics show the spacecraft to be in an inherently unstable equilibrium orientation. Control, based on the FLT, is then applied to restore the desired attitude of the spacecraft. The performance of three sets of control gains are compared. Even if the satellite is initially subjected to a large disturbance of 1° in pitch, roll, and yaw, the controller is successful in reducing the attitude err...

On the nonlinear slewing dynamics and control of the Space Station based Mobile Servicing System

A relatively general Lagrangian formulation for studying the nonlinear dynamics and control of space-craft with interconnected flexible members in a tree-type topology is developed. Versatility of the formulation is illustrated through a dynamical study of the Space Station based two-link Mobile Servicing System (MSS). The performance of the MSS undergoing inplane and out-of-plane slewing maneuvers is compared. Results indicate that, in absence of control, the maneuvers induce undesirable librational motion of the Space Station as well as vibration of the links. Nonlinear control, based on the Feedback Linearization Technique (FLT), appears promising. Quasi-Closed Loop Control (QCLC), a variation of the FLT, is applied to control the libration of the Space Station. Once the attitude of the Space Station is controlled, the performance of the MSS improves significantly. For a 5-minute maneuver of the MSS, the maximum control torque required is only 34.5 Nm.