Robust trajectory control of a robot manipulator
01 Nov 1991-International Journal of Systems Science (Taylor & Francis Group)-Vol. 22, Iss: 11, pp 2185-2194
TL;DR: In this paper, a control scheme for a robotic manipulator with uncertain dynamics is considered, the controller gains are updated to cow with variations in the manipulator inverse due to changes the operating point, a feedback conlroller that provides arbitrary assignment of all eigenvalues and certain parts o f 3 closed-loop eigenvector structure: is also used.
Abstract: The tracking problem for a robotic manipulator with uncertain dynamics is considered. The proposed control scheme utilizes manipulator ‚inverse‘ as an adaptive feedforward controller, the controller gains are updated to cow with variations in the manipulator inverse due to changes the operating point A feedback conlroller that provides arbitrary assignment of all eigenvalues and certain parts o f 3 closed-loop eigenvector structure: is also used. Eigenstructure assignment is used to enhance closed-loop stability and to achieve robust tracking. Simulation results are presented in support of the proposed control scheme. The results demonstrate satisfactory performance of the controller despite variations in payload.
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01 Jan 1996TL;DR: This dissertation presents an approach to simulating the dynamic force and moment interaction between a human and a virtual object using a robotic manipulator as the force transmitter and demonstrates the feasibility of automatic, computer generated control laws for complex robotic systems.
Abstract: This dissertation presents an approach to simulating the dynamic force and moment interaction between a human and a virtual object using a robotic manipulator as the force transmitter. Accurate control of the linear and angular accelerations of the robot end effector is required in order for the correct forces and moments to be imparted on a human operating in a computer generated virtual environment. A control system has been designed which is robust in terms of stability and performance. This control system is derived from abbreviated linear and nonlinear models of the manipulator dynamics which are efficient enough for real-time implementation yet retain a sufficient level of complexity for accurate calculations. An efficient multiple-input multiple-output (MIMO) pole placement scheme has also been devised which locates the pre-specified system eigenvalues. The controller gains are given as explicit functions of a desired trajectory to be followed and, thus, are time varying such that the overall closed-loop system is rendered time-invariant. Key software elements were automatically derived and output in compiler-ready form demonstrating the feasibility of automatic, computer generated control laws for complex robotic systems. Test results are given for a PUMA 560 used to impart dynamic forces on a user operating in a virtual environment.
26 citations
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01 Jan 1992
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
10 citations
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TL;DR: It has been shown that a set of LTI systems in block companion form is simultaneously quadratically stabilizable by a single static state feedback controller, and a new approach to robot tracking controller design is presented.
Abstract: In this paper, we consider the simultaneous quadratic stabilization problem for a class of linear time-invariant (LTI) systems. It has been shown that a set of LTI systems in block companion form is simultaneously quadratically stabilizable by a single static state feedback controller. Based on this result, a new approach to robot tracking controller design is presented. The proposed control scheme consists of a feedforward controller based on the inverse dynamics of the robot and a feedback controller. The nonlinear model of the robot is viewed as piecewise LTI systems obtained by linearizing the model at selected number of points on a specified trajectory in the joint space. The collection of all the LTI systems constitutes a set in which each member is observed to be in block companion form. For this class of systems, an algorithm for the design of a single stabilizing feedback controller is presented. A numerical example of a two link manipulator has been considered to validate the proposed theory.
3 citations
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TL;DR: In this paper, a computation-effective control design procedure for eigenstructure assignment using aggregation is presented, where Dominant eigenvalues are placed at specified locations in the complex plane and the non-dominant eigen values are placed in a specified disk.
Abstract: Design procedures based on exact eigenstructure assignment are not suitable because of very high computational requirements. A computation-effective control design procedure for eigenstructure assignment using aggregation is presented. Dominant eigenvalues are placed at specified locations in the complex plane and the non-dominant eigenvalues are placed in a specified disk. The proposed design procedure is applied to the trajectory tracking problem of a robot manipulator. An error-pattern based payload estimation and compensation scheme is also proposed to improve performance robustness.
2 citations
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13 Sep 1993TL;DR: In this article, a sliding mode observer is introduced to make the error dynamics uniformly ultimately bounded, which can be applied to the control of an n-link robot arm with unknown but bounded payload and disturbance.
Abstract: This paper discusses the problem of robust control in robotic manipulator systems. The designing process can be viewed as a modified computed torque method. By introducing a sliding mode observer, we construct a robust controller which makes the error dynamics uniformly ultimately bounded. The scheme can be applied to the control of n-link robot arm with unknown but bounded payload and disturbance. Simulation of a 2-link robot arm is done. >
References
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01 Jan 1983
TL;DR: Theoretical Equivalence of Mayer, Lagrange, and Bolza Problems of Optimal Control, and the Necessary Conditions and Sufficient Conditions Convexity and Lower Semicontinuity.
Abstract: 1 Problems of Optimization-A General View.- 1.1 Classical Lagrange Problems of the Calculus of Variations.- 1.2 Classical Lagrange Problems with Constraints on the Derivatives.- 1.3 Classical Bolza Problems of the Calculus of Variations.- 1.4 Classical Problems Depending on Derivatives of Higher Order.- 1.5 Examples of Classical Problems of the Calculus of Variations.- 1.6 Remarks.- 1.7 The Mayer Problems of Optimal Control.- 1.8 Lagrange and Bolza Problems of Optimal Control.- 1.9 Theoretical Equivalence of Mayer, Lagrange, and Bolza Problems of Optimal Control. Problems of the Calculus of Variations as Problems of Optimal Control.- 1.10 Examples of Problems of Optimal Control.- 1.11 Exercises.- 1.12 The Mayer Problems in Terms of Orientor Fields.- 1.13 The Lagrange Problems of Control as Problems of the Calculus of Variations with Constraints on the Derivatives.- 1.14 Generalized Solutions.- Bibliographical Notes.- 2 The Classical Problems of the Calculus of Variations: Necessary Conditions and Sufficient Conditions Convexity and Lower Semicontinuity.- 2.1 Minima and Maxima for Lagrange Problems of the Calculus of Variations.- 2.2 Statement of Necessary Conditions.- 2.3 Necessary Conditions in Terms of Gateau Derivatives.- 2.4 Proofs of the Necessary Conditions and of Their Invariant Character.- 2.5 Jacobi's Necessary Condition.- 2.6 Smoothness Properties of Optimal Solutions.- 2.7 Proof of the Euler and DuBois-Reymond Conditions in the Unbounded Case.- 2.8 Proof of the Transversality Relations.- 2.9 The String Property and a Form of Jacobi's Necessary Condition.- 2.10 An Elementary Proof of Weierstrass's Necessary Condition.- 2.11 Classical Fields and Weierstrass's Sufficient Conditions.- 2.12 More Sufficient Conditions.- 2.13 Value Function and Further Sufficient Conditions.- 2.14 Uniform Convergence and Other Modes of Convergence.- 2.15 Semicontinuity of Functionals.- 2.16 Remarks on Convex Sets and Convex Real Valued Functions.- 2.17 A Lemma Concerning Convex Integrands.- 2.18 Convexity and Lower Semicontinuity: A Necessary and Sufficient Condition.- 2.19 Convexity as a Necessary Condition for Lower Semicontinuity.- 2.20 Statement of an Existence Theorem for Lagrange Problems of the Calculus of Variations.- Bibliographical Notes.- 3 Examples and Exercises on Classical Problems.- 3.1 An Introductory Example.- 3.2 Geodesics.- 3.3 Exercises.- 3.4 Fermat's Principle.- 3.5 The Ramsay Model of Economic Growth.- 3.6 Two Isoperimetric Problems.- 3.7 More Examples of Classical Problems.- 3.8 Miscellaneous Exercises.- 3.9 The Integral I = ?(x?2 ? x2)dt.- 3.10 The Integral I = ?xx?2dt.- 3.11 The Integral I = ?x?2(1 + x?)2dt.- 3.12 Brachistochrone, or Path of Quickest Descent.- 3.13 Surface of Revolution of Minimum Area.- 3.14 The Principles of Mechanics.- Bibliographical Notes.- 4 Statement of the Necessary Condition for Mayer Problems of Optimal Control.- 4.1 Some General Assumptions.- 4.2 The Necessary Condition for Mayer Problems of Optimal Control.- 4.3 Statement of an Existence Theorem for Mayer's Problems of Optimal Control.- 4.4 Examples of Transversality Relations for Mayer Problems.- 4.5 The Value Function.- 4.6 Sufficient Conditions.- 4.7 Appendix: Derivation of Some of the Classical Necessary Conditions of Section 2.1 from the Necessary Condition for Mayer Problems of Optimal Control.- 4.8 Appendix: Derivation of the Classical Necessary Condition for Isoperimetric Problems from the Necessary Condition for Mayer Problems of Optimal Control.- 4.9 Appendix: Derivation of the Classical Necessary Condition for Lagrange Problems of the Calculus of Variations with Differential Equations as Constraints.- Bibliographical Notes.- 5 Lagrange and Bolza Problems of Optimal Control and Other Problems.- 5.1 The Necessary Condition for Bolza and Lagrange Problems of Optimal Control.- 5.2 Derivation of Properties (P1?)-(P4?) from (P1)-(P4).- 5.3 Examples of Applications of the Necessary Conditions for Lagrange Problems of Optimal Control.- 5.4 The Value Function.- 5.5 Sufficient Conditions for the Bolza Problem.- Bibliographical Notes.- 6 Examples and Exercises on Optimal Control.- 6.1 Stabilization of a Material Point Moving on a Straight Line under a Limited External Force.- 6.2 Stabilization of a Material Point under an Elastic Force and a Limited External Force.- 6.3 Minimum Time Stabilization of a Reentry Vehicle.- 6.4 Soft Landing on the Moon.- 6.5 Three More Problems on the Stabilization of a Point Moving on a Straight Line.- 6.6 Exercises.- 6.7 Optimal Economic Growth.- 6.8 Two More Classical Problems.- 6.9 The Navigation Problem.- Bibliographical Notes.- 7 Proofs of the Necessary Condition for Control Problems and Related Topics.- 7.1 Description of the Problem of Optimization.- 7.2 Sketch of the Proofs.- 7.3 The First Proof.- 7.4 Second Proof of the Necessary Condition.- 7.5 Proof of Boltyanskii's Statements (4.6.iv-v).- Bibliographical Notes.- 8 The Implicit Function Theorem and the Elementary Closure Theorem.- 8.1 Remarks on Semicontinuous Functionals.- 8.2 The Implicit Function Theorem.- 8.3 Selection Theorems.- 8.4 Convexity, Caratheodory's Theorem, Extreme Points.- 8.5 Upper Semicontinuity Properties of Set Valued Functions.- 8.6 The Elementary Closure Theorem.- 8.7 Some Fatou-Like Lemmas.- 8.8 Lower Closure Theorems with Respect to Uniform Convergence.- Bibliographical Notes.- 9 Existence Theorems: The Bounded, or Elementary, Case.- 9.1 Ascoli's Theorem.- 9.2 Filippov's Existence Theorem for Mayer Problems of Optimal Control.- 9.3 Filippov's Existence Theorem for Lagrange and Bolza Problems of Optimal Control.- 9.4 Elimination of the Hypothesis that A Is Compact in Filippov's Theorem for Mayer Problems.- 9.5 Elimination of the Hypothesis that A Is Compact in Filippov's Theorem for Lagrange and Bolza Problems.- 9.6 Examples.- Bibliographical Notes.- 10 Closure and Lower Closure Theorems under Weak Convergence.- 10.1 The Banach-Saks-Mazur Theorem.- 10.2 Absolute Integrability and Related Concepts.- 10.3 An Equivalence Theorem.- 10.4 A Few Remarks on Growth Conditions.- 10.5 The Growth Property (?) Implies Property (Q).- 10.6 Closure Theorems for Orientor Fields Based on Weak Convergence.- 10.7 Lower Closure Theorems for Orientor Fields Based on Weak Convergence.- 10.8 Lower Semicontinuity in the Topology of Weak Convergence.- 10.9 Necessary and Sufficient Conditions for Lower Closure.- Bibliographical Notes.- 11 Existence Theorems: Weak Convergence and Growth Conditions.- 11.1 Existence Theorems for Orientor Fields and Extended Problems.- 112 Elimination of the Hypothesis that A Is Bounded in Theorems (11.1. i-iv).- 11.3 Examples.- 11.4 Existence Theorems for Problems of Optimal Control with Unbounded Strategies.- 11.5 Elimination of the Hypothesis that A Is Bounded in Theorems (11.4.i-v).- 11.6 Examples.- 11.7 Counterexamples.- Bibliographical Notes.- 12 Existence Theorems: The Case of an Exceptional Set of No Growth.- 12.1 The Case of No Growth at the Points of a Slender Set. Lower Closure Theorems..- 12.2 Existence Theorems for Extended Free Problems with an Exceptional Slender Set.- 12.3 Existence Theorems for Problems of Optimal Control with an Exceptional Slender Set.- 12.4 Examples.- 12.5 Counterexamples.- Bibliographical Notes.- 13 Existence Theorems: The Use of Lipschitz and Tempered Growth Conditions.- 13.1 An Existence Theorem under Condition (D).- 13.2 Conditions of the F, G, and H Types Each Implying Property (D) and Weak Property (Q).- 13.3 Examples.- Bibliographical Notes.- 14 Existence Theorems: Problems of Slow Growth.- 14.1 Parametric Curves and Integrals.- 14.2 Transformation of Nonparametric into Parametric Integrals.- 14.3 Existence Theorems for (Nonparametric) Problems of Slow Growth.- 14.4 Examples.- Bibliographical Notes.- 15 Existence Theorems: The Use of Mere Pointwise Convergence on the Trajectories.- 15.1 The Helly Theorem.- 15.2 Closure Theorems with Components Converging Only Pointwise.- 15.3 Existence Theorems for Extended Problems Based on Pointwise Convergence.- 15.4 Existence Theorems for Problems of Optimal Control Based on Pointwise Convergence.- 15.5 Exercises.- Bibliographical Notes.- 16 Existence Theorems: Problems with No Convexity Assumptions.- 16.1 Lyapunov Type Theorems.- 16.2 The Neustadt Theorem for Mayer Problems with Bounded Controls.- 16.3 The Bang-Bang Theorem.- 16.4 The Neustadt Theorem for Lagrange and Bolza Problems with Bounded Controls.- 16.5 The Case of Unbounded Controls.- 16.6 Examples for the Unbounded Case.- 16.7 Problems of the Calculus of Variations without Convexity Assumptions.- Bibliographical Notes.- 17 Duality and Upper Semicontinuity of Set Valued Functions.- 17.1 Convex Functions on a Set.- 17.2 The Function T(x z).- 17.3 Seminormality.- 17.4 Criteria for Property (Q).- 17.5 A Characterization of Property (Q) for the Sets $$\tilde Q$$(t, x) in Terms of Seminormality.- 17.6 Duality and Another Characterization of Property (Q) in Terms of Duality.- 17.7 Characterization of Optimal Solutions in Terms of Duality.- 17.8 Property (Q) as an Extension of Maximal Monotonicity.- Bibliographical Notes.- 18 Approximation of Usual and of Generalized Solutions.- 18.1 The Gronwall Lemma.- 18.2 Approximation of AC Solutions by Means of C1 Solutions.- 18.3 The Brouwer Fixed Point Theorem.- 18.4 Further Results Concerning the Approximation of AC Trajectories by Means of C1 Trajectories.- 18.5 The Infimum for AC Solutions Can Be Lower than the One for C1 Solutions.- 18.6 Approximation of Generalized Solutions by Means of Usual Solutions.- 18.7 The Infimum for Generalized Solutions Can Be Lower than the One for Usual Solutions.- Bibliographical Notes.- Author Index.
2,371 citations
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TL;DR: This book discusses the construction of mental ray, a model for synthetic lighting, and some of the techniques used to design and implement such models.
Abstract: Introduction. Chapter 1: Introduction to mental ray. What Is mental ray? Why Use mental ray? The Structure of mental ray. mental ray Integration. Command-Line Rendering and the Stand-Alone Renderer. mental ray Shaders and Shader Libraries. Indirect Illumination. Chapter 2: Rendering Algorithms. Introduction to Synthetic Lighting. Rendering under the Hood. mental ray Rendering Algorithms. Scanline Rendering in Depth. Raytrace Rendering in Depth. Hardware Rendering. Chapter 3: mental ray Output. mental ray Data Types. The Frame Buffer. Frame Buffer Options. mental ray Cameras. Output Statements. Chapter 4: Camera Fundamentals. Camera Basics and Aspect Ratios. Camera Lenses. Host Application Settings. Chapter 5: Quality Control. Sampling and Filtering in Host Applications. Raytrace Acceleration. Diagnostic and BSP Fine-Tuning. Chapter 6: Lights and Soft Shadows. mental ray Lights. Area Lights. Host Application Settings. Light Profiles. Chapter 7: Shadow Algorithms. Shadow Algorithms. Raytrace Shadows. Depth-Based Shadows. Stand-Alone and Host Settings. Chapter 8: Motion Blur. mental ray Motion Blur. Motion-Blur Options. Motion-Blur Render Algorithms. Host Settings. Chapter 9: The Fundamentals of Light and Shading Models. The Fundamentals of Light. Light Transport and Shading Models. mental ray Shaders. Chapter 10: mental ray Shaders and Shader Trees. Installing Custom Shaders. DGS and Dielectric Shading Models. Glossy Reflection and Refraction Shaders. Brushed Metals with the Glossy and Anisotropic Shaders. The Architectural (mia) Material. Chapter 11: mental ray Textures and Projections. Texture Space and Projections. mental ray Bump Mapping. mental ray Projection and Remapping Shaders. Host Application Settings. Memory Mapping, Pyramid Images, and Image Filtering. Chapter 12: Indirect Illumination. mental ray Indirect Illumination. Photon Shaders and Photon-Casting Lights. Indirect Illumination Options and Fine-Tuning. Participating Media (PM) Effects. Chapter 13: Final Gather and Ambient Occlusion. Final Gather Fundamentals. Final Gather Options and Techniques. Advanced Final Gather Techniques. Ambient Occlusion. Chapter 14: Subsurface Scattering. Advanced Shading Models. Nonphysical Subsurface Scattering. An Advanced Shader Tree. Physical Subsurface Scattering. Appendix: About the Companion CD. Index.
1,022 citations
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01 Sep 1987TL;DR: What is believed to be the first golbally convergent, rigorous proof of the stability of such a scheme in its non-linear setting, as well as its asymptotic properties and conditions for parameter convergence are presented.
Abstract: We present an adaptive version of the computed torque method for the control of manipulators with rigid links. The algorithun estimates parameters on-line which appear in the non-linear dynamic model of the manipulator, such as load and link mass parameters and friction parameters, and uses the latest estimates in the computed torque servo. We present what we believe is the first golbally convergent, rigorous proof of the stability of such a scheme in its non-linear setting, as well as its asymptotic properties and conditions for parameter convergence. We illustrate the theory with some simulation results.
862 citations
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01 Jan 1984
TL;DR: Practical control problems from various engineering disciplines have been drawn to illustrate the potential concepts and most of the theoretical results have been presented in a manner suitable for digital computer programming along with the necessary algorithms for numerical computations.
Abstract: From the Publisher:
The book provides an integrated treatment of continuous-time and discrete-time systems for two courses at postgraduate level, or one course at undergraduate and one course at postgraduate level. It covers mainly two areas of modern control theory, namely: system theory, and multivariable and optimal control. The coverage of the former is quite exhaustive while that of latter is adequate with significant provision of the necessary topics that enables a research student to comprehend various technical papers. The stress is on the interdisciplinary nature of the subject. Practical control problems from various engineering disciplines have been drawn to illustrate the potential concepts. Most of the theoretical results have been presented in a manner suitable for digital computer programming along with the necessary algorithms for numerical computations.
204 citations
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TL;DR: In this article, a simple scheme for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates is presented, which consists of two independent multi-ivariable feedforward and feedback controllers.
Abstract: The paper presents simple schemes for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates. The joint control scheme consists of two independent multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms - implying feedforward from the desired position, velocity and acceleration. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and is designed to achieve pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. Simple and explicit expressions of computation of the feedforward and feedback gains are obtained based on the linearized model of robot dynamics. This leads to computationally efficient schemes for either on-line gain computation or off-line gain scheduling to account for variations in the linearized robot model due to changes in the operating point. The joint control scheme is extended to direct control of the end-effector motion in Cartesian space. Simulation results are given for illustration.
40 citations