On adaptive inverse dynamics for free-floating space manipulators

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Abstract

This paper is devoted to the investigation of adaptive inverse dynamics for free-floating space manipulators (FFSMs) suffering from parameter uncertainties/variations. To overcome the nonlinear parametric problem of the dynamics of FFSMs, we introduce a new regressor matrix called the generalized dynamic regressor. Based on this regressor, and with Lyapunov stability analysis tools, we obtain a new parameter adaptation law and show that the closed-loop system is stable, and that the joint tracking errors converge asymptotically to zero. Simulation results are provided to illustrate the performance of the proposed adaptive algorithm. Furthermore, we conduct a comparative study between adaptive inverse dynamics, prediction error based adaptation, and passivity based adaptation.

Highlights

► We propose an adaptive inverse dynamics controller for free-floating space robots. ► A new dynamic regressor is proposed to conquer the nonlinearly parametric problem. ► A novel parameter adaptation law is derived using Lyapunov stability tools. ► We conduct comparative studies between the proposed approach and the existing ones.

Introduction

Robotics in space circumstances/environments is usually mounted on a movable spacecraft to execute tasks, and such robotic–spacecraft systems are the well-known space manipulators. The initiative purpose of using space manipulators is to extend human manipulation in cost-expensive and hazardous space environments, e.g., transferring payloads from one place to another, conducting on-orbit servicing, executing maintenance and construction for the International Space Station (ISS), and maneuvering tumbling spacecraft. Performing such tasks inherently faces the problem of dynamic parameter variations, which make model based controllers (e.g., computed torque control) [1], [2] insufficient for accuracy/performance requirements or even unstable in some cases. Among many candidate approaches to this problem, adaptive control bears its own superiorities, which continues to improve the performance of the system through on-line adaptation to the unknown dynamic properties of the manipulator.

The inverse dynamics control is well known in robotics, and is also called the computed torque control. In the ideal case of accurate knowledge of robot parameters, the inverse dynamics controller gives rise to a linear and decoupled error dynamics [2], [3], [4]. For tackling parameter variation/uncertainty, two categories of adaptive inverse dynamics controllers (which are classified based on their respective adaptation rules, see [5] for the detail) have been provided to ensure the manipulator performance. In the first category, the parameter adaptations are driven by tracking errors [3], [4]. The major objective of the adaptation scheme in [3], [4] is to reduce the manipulator joint tracking errors. In the second category, the driving signals of parameter adaptations are prediction errors of the filtered joint torque [6], [7]. The prediction error based controller given in [6] is composed of a modified computed torque controller and a modified least-square parameter estimator. The global convergence of the closed-loop robotic system is obtained via input–output stability theory. Later, Li and Slotine [7] improved the controller structure of [6] in a way such that the computation of the inverse of the estimated inertia matrix is avoided. Furthermore, a novel parameter estimation approach, which can guarantee the uniform positive definiteness of the estimated inertia matrix, has been presented.

Generally, model based controllers of fixed-base manipulators can be straightforwardly extended to free-floating space robots since the basic dynamic structure of a free-floating system is almost identical to that of a fixed-base manipulator system, as illustrated in [8]. However, in the presence of parameter uncertainties or variations, the control schemes for free-floating manipulators and those for fixed-base manipulators become somewhat different. The major problem encountered is the nonlinearly parametric property of the dynamics of free-floating manipulators, which hinders the application of the conventional adaptive control algorithms based on the linearly parametric dynamic model [9], [10]. The first adaptive controller attempting to resolve this problem was the normal form augmentation based algorithm in [10] under the passivity based adaptation framework, and later in [11] under the prediction error based adaptation framework. This approach uses the extended model of the free-floating manipulator to derive the control law and the adaptation law. But it needs to measure spacecraft accelerations, and the condition of ensuring the system’s stability is also quite stringent due to the use of acceleration signals in the control torque input. Recently, passivity based control without the use of spacecraft acceleration signals was proposed in [12] and in [13] under the framework of the inverted chain approach. Moreover, prediction error based adaptive control for task-space trajectory tracking of free-floating space manipulators was presented in [14], where the prediction error of the filtered control input was employed for parameter adaptation.

Motivated by previous work, in this paper, we will propose a novel adaptive inverse dynamics controller for free-floating space manipulators using linear parametrization based adaptive methodology (this was once thought to be impossible due to the nonlinearly parametric nature of the FFSM dynamics [9]), which extends the adaptive inverse dynamics for fixed-base robots [3] to FFSMs with nonlinearly parametric dynamics. The basic controller structure is shown to be the certainty-equivalence form of the computed torque controller for FFSMs, and we establish a new dynamic regressor matrix that we call the generalized dynamic regressor, based on which we derive the adaptation laws via Lyapunov stability tools. The major advantage of the proposed adaptive inverse dynamics controller over the previous passivity based controller [12] is that it leads to a linear and decoupled error dynamics in the case of full knowledge of the dynamic properties. At this place, we should say that the prediction error based adaptive controller [14] and the adaptive inverse dynamics algorithm that will be studied in this paper should belong to the same framework, e.g., adaptive inverse dynamics. The difference lies in the driving signals for the parameter adaptation, and whether or not requiring the measurement of the acceleration signals for the parameter estimation. Thus, another major purpose of this work is to present a comparative study between these three adaptive control schemes.

Section snippets

Dynamic model of free-floating space manipulators

The equations of motion of an n-DOF (degree of freedom) FFSM explicitly involving the rotational motion of the spacecraft can be written as [15], [16]M(qm)q̈+C(qm,q̇)q̇=τ, where qmRn is the joint configuration variable of the manipulator, q̇=[q̇bTq̇mT]T, q̇b=ωbR3 is the spacecraft angular velocity, q̇m=ddtqmRn is the joint velocity of the manipulator, M(qm)=[MbbMbmMbmTMmm]R(n+3)×(n+3) is the inertia matrix, C(qm,q̇)=[CbbCbmCmbCmm] is the centrifugal and Coriolis matrix, MbbRn×n is the

Inverse dynamics for free-floating space manipulators

In this section, we investigate the adaptive inverse dynamics control for free-floating manipulators. The FFSM is required to asymptotically track a time-varying desired joint trajectory qmdRn, and it is assumed that qmd,q̇md,q̈md are all bounded signals.

Before proceeding into the adaptive inverse dynamics controller design, we first revisit the basic idea of the well-known inverse dynamics in the case that the FFSM parameters are accurately known.

Simulation results and discussions

In this section, we examine the performance of the proposed adaptive inverse dynamics controller through simulations on a two-DOF space manipulator gripping an unknown load, shown in Fig. 1. Moreover, we do comparisons between the proposed direct adaptive inverse dynamics control, prediction error based adaptive inverse dynamics (29), and passivity based control [12] (its joint-space version [14]). The physical parameters of the space manipulator are listed in Table 1, where mi and IC,i(i=0,1,2)

Concluding remarks

In this paper, we have proposed an adaptive inverse dynamics control for free-floating space manipulators with uncertain dynamics. With Lyapunov stability theory, we derived the parameter adaptation law via defining a new dynamic regressor matrix called the generalized dynamic regressor. We show that the closed-loop system is stable, and that the joint tracking errors asymptotically converge to zero. Using a two-DOF planar space manipulator, we illustrate the performance of the proposed

Acknowledgment

This research is supported by the National Natural Science Foundation of China under grants 61004058 and 60804016.

Hanlei Wang received his B.S. degree in Mechanical Engineering from Shijiazhuang Railway Institute, China, in 2004, his M.S. degree in Mechanical Engineering from Harbin Institute of Technology, China, in 2006, and his Ph.D. in Control Theory and Control Engineering from Beijing Institute of Control Engineering, China Academy of Space Technology, in 2009. Since 2009, he has been with Beijing Institute of Control Engineering as a Research Engineer. His research interests are adaptive control

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    Hanlei Wang received his B.S. degree in Mechanical Engineering from Shijiazhuang Railway Institute, China, in 2004, his M.S. degree in Mechanical Engineering from Harbin Institute of Technology, China, in 2006, and his Ph.D. in Control Theory and Control Engineering from Beijing Institute of Control Engineering, China Academy of Space Technology, in 2009. Since 2009, he has been with Beijing Institute of Control Engineering as a Research Engineer. His research interests are adaptive control theory and its applications in robotics, space robotics and spacecraft, synchronization of networked robotics and multi-agent systems.

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