Comparative study on linearized robot models
01 Jun 1993-Journal of Intelligent and Robotic Systems (Springer Science and Business Media LLC)-Vol. 7, Iss: 3, pp 287-300
TL;DR: It is shown that the rate linearization method leads to a satisfactory tradeoff between computation, accuracy, and stability in the case of high velocity motions.
Abstract: For representing the input—output behaviour of a robot manipulator by a linear time-invariant model, four direct linearization schemes are: (i) state linearization, (ii) linearization based on an identification method, (iii) linearization based on neglecting velocity-dependent and gravity terms and (iv) linearization based on neglecting the velocity-dependent term only (rate linearization). In order to make an appropriate choice of linear model for the development of real-time control, these schemes are extensively studied in this paper. It is shown that the rate linearization method leads to a satisfactory tradeoff between computation, accuracy, and stability. In the case of high velocity motions, a combination of state linearization and rate linearization is proposed.
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Patent•
21 Jul 2011
TL;DR: In this article, a system for performing a medical procedure comprising at least one tool and a tool support for supporting a distal portion of the tool is described, where an operator manipulates a human interface device and produces control signals sent to a controller.
Abstract: A system for performing a medical procedure is provided comprising at least one tool and a tool support for supporting a distal portion of the tool. An operator manipulates a human interface device and produces control signals sent to a controller. The controller manipulates the tool support based on the received control signals.
26 citations
01 Dec 2011
TL;DR: Simulations and experimental results of an upper limb exoskeleton give validation of the iterative tuning method of PID control for the robot manipulator based on the responses of the closed loop system.
Abstract: This paper addresses the iterative tuning method of PID control for the robot manipulator based on the responses of the closed loop system. Several properties of the robot control are used, such as any PD control can stabilize a robot in regulation case, the colsed-loop system of PID control can be approximated by a linear system, and the control torque to the robot manipulator is linearly independent of the robot dynamic. By using these properties, a novel systematic turning method for the PID control is proposed. Simulations and experimental results of an upper limb exoskeleton give validation of this PID tuning method.
25 citations
Cites background from "Comparative study on linearized rob..."
...But many experiments, see Swarup and Gopal (1993), showed that even at low speeds ( ̇) should be accounted for....
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TL;DR: A new systematic tuning method of PID control for robot manipulators that is simple, systematic, and stable and the transient properties of this PID control are better than the other normal PID controllers.
Abstract: Purpose – This paper aims to address a new iterative tuning method of PID control for robot manipulators. Design/methodology/approach – This tuning method uses several properties of the robot control, such as any PD control can stabilize a robot in regulation case, the closed-loop system of PID control can be approximated by a linear system, the control torque to the robot manipulator is linearly independent of the robot dynamic. Findings – Compared with the other PID tuning methods, this novel method is simple, systematic, and stable. The transient properties of this PID control are better than the other normal PID controllers. Originality/value – In this paper, a new systematic tuning method for PID control is proposed. The paper applies this method on an upper limb exoskeleton, and real experiment results give validation of our PID tuning method.
23 citations
Patent•
21 Oct 2011
TL;DR: In this paper, a highly articulated robotic probe comprises an outer sleeve and an inner core, which are configured to pivot relative to one another and each of the links determine the overall pivot angle.
Abstract: A highly articulated robotic probe comprises an outer sleeve and an inner core. The outer sleeve and inner core include a plurality of links. The links of the outer sleeve and inner core are configured to pivot relative to one another. Various characteristics of the links determine the overall pivot angle of the articulated probe. Each of the plurality of links may have one or more channels. The channels form a semi-continuous passage from link to link and are configured to receive an elongated member such as an inner core, tool or cable. One or more cables may be used to control the outer links of the outer sleeve and the inner links of the inner core. Various characteristics of the cables determine the overall performance of the articulated probe.
22 citations
TL;DR: This work proposes a novel method to design task space controllers without using the complete knowledge of the mechanism dynamics and linearization methods, and uses pole placement and sliding mode controllers whose gains are tuned according to the slider dynamics.
Abstract: In this work, a position control in task space for slider-crank mechanisms is presented. In order to apply linear controllers it is required to linearize the mechanism dynamics at an equilibrium point. However, complete dynamic knowledge is needed and the linearization technique gives an oversimplified model that affects the control performance. In this work, it is proposed a novel method to design task space controllers without using the complete knowledge of the mechanism dynamics and linearization methods. From the extended dynamic model of parallel robots, it can be seen that the end-effector (slider) dynamics is expressed as a linear system that can be used directly for the control design instead of the complete mechanism linear dynamics. The approach requires a minimal knowledge of the mechanism dynamics and avoids linearization methods. To verify our approach, it is used pole placement and sliding mode controllers whose gains are tuned according to the slider dynamics. A linear sensor is mounted at the slider to measure its position and avoids considering noise and disturbances at links before the slider. Simulations and experiments are presented to validate our approach using two kinds of slider-crank mechanisms.
17 citations
Cites background from "Comparative study on linearized rob..."
...another way to linearize the dynamics [17], but it has been shown that the Coriolis effect even at low speeds should be accounted for [18]....
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References
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Book•
01 Jan 1986
TL;DR: This chapter discusses Jacobians: Velocities and Static Forces, Robot Programming Languages and Systems, and Manipulator Dynamics, which focuses on the role of Jacobians in the control of Manipulators.
Abstract: 1. Introduction. 2. Spatial Descriptions and Transformations. 3. Manipulator Kinematics. 4. Inverse Manipulator Kinematics. 5. Jacobians: Velocities and Static Forces. 6. Manipulator Dynamics. 7. Trajectory Generation. 8. Manipulator Mechanism Design. 9. Linear Control of Manipulators. 10. Nonlinear Control of Manipulators. 11. Force Control of Manipulators. 12. Robot Programming Languages and Systems. 13. Off-Line Programming Systems.
5,992 citations
"Comparative study on linearized rob..." refers background in this paper
...Introduction The nonlinear and coupled dynamics of a robot manipulator having n joints can be represented in the general form [1]: M(O)O + N(O, O) + G(O) = T, (1) where M(O) is the n x n inertia matrix, N(O, O) is the n x 1 Coriolis, centrifugal, and frictional torque vector, G(O) is the n x 1 gravity loading vector, and T is the n x 1 joint torque vector....
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...Appendix A Consider the frictionless two link manipulator in a vertical plane with dynamic equations of motion given by [1] MI,'O, + M~z02 + Ul + GI = T1, (A1) M21"01 + M:20: + N2 + 62 = T2, where M11 = aj + a 2 COS 02, M12 = Mzl = a3 + (az/2) cos02, M22 = a3 NI = - ( a2 sin 02)(0102 + 0~/2), N2 = (a2 sin 02)(0~/2), G~ = a4 cos 01 + a5 cos (0j + 02)7 G 2 = a 5c0s(01 + 02) al, a2 ....
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Book•
01 Jul 1987
1,480 citations
"Comparative study on linearized rob..." refers methods in this paper
...A Linear Control Scheme The linear control scheme [2] used in this paper consists of linear model, feedforward control, and feedback control....
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01 Apr 1989
TL;DR: It is shown that the computed-torque scheme outperforms the independent joint control scheme as long as there is not torque saturation in the actuators and the importance of compensating for the nonlinear Coriolis and centrifugal forces even at low speeds of operation is established.
Abstract: Experimental results on the real-time performance of model-based control algorithms are presented. The computed-torque scheme which utilizes the complete dynamics model of the manipulator was compared to the independent joint control scheme, which assumes a decoupled and linear model of the manipulator dynamics. The two manipulator control schemes have been implemented on the Carnegie-Mellon University DD (direct-drive) Arm II with a sampling period of 2 ms. The authors discuss the design of controller gains for both the computed-torque and the independent joint control schemes and establish a framework for comparing their trajectory-tracking performances. It is shown that the computed-torque scheme outperforms the independent joint control scheme as long as there is not torque saturation in the actuators. Based on the experimental results, the authors conclusively establish the importance of compensating for the nonlinear Coriolis and centrifugal forces even at low speeds of operation. >
83 citations
"Comparative study on linearized rob..." refers background in this paper
...[7], the velocity-dependent term can be neglected, whereas Khosla and Kanade [8] have concluded that it should be accounted for, even at low speeds....
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...Also, Khosla and Kanade [8] reported that at constant speeds, these velocity-dependent forces are dominant....
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55 citations
"Comparative study on linearized rob..." refers methods in this paper
...This is a rate linearization scheme [6] which results in a linear model of the form AO + Cq = u, (12) where [ ~a(o) ] A = [M(0)] e and C = L ~0 Je" Using :a rate linearized model with the tracking control, the response for the exponential trajectory is given in Figure 3....
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Book•
01 Jan 1991
TL;DR: A Cartesian Tensor Approach for Solving the IDP and a Recursive Lagrangian Formulation on Moment Vectors and Generalized Forces.
Abstract: 1 Introduction.- 1.1 Basic Problems in Robot Manipulator Dynamics.- 1.2 General Remarks on Robot Manipulator Dynamics.- 1.3 Objectives and Motivation.- 1.4 Preview.- 1.5 References.- 2 Notation, Terminology and Background Material.- 2.1 Notation.- 2.2 Rigid Bodies and their Finite Displacement.- 2.3 Robot Manipulators.- 2.4 References.- 3 Cartesian Tensor Analysis.- 3.1 Introduction.- 3.2 Second Order Cartesian Tensors.- 3.3 Properties of Second Order Cartesian Tensors.- 3.4 Cartesian Tensor Algebraic Identities.- 3.5 References.- 4 Cartesian Tensors and Rigid Body Motion.- 4.1 Introduction.- 4.2 On Kinematic Analysis of Rigid Body Motion.- 4.3 On Dynamic Analysis of Rigid Body Motion.- 4.4 References.- 5 Manipulator Inverse Dynamics.- 5.1 Introduction.- 5.2 Previous Results and General Observations on Manipulator Inverse Dynamics.- 5.3 A Cartesian Tensor Approach for Solving the IDP.- 5.4 The Use of Euler-Lagrange and Kane's Formulations in Deriving Algorithm 5.7.- 5.5 Concluding Remarks.- 5.6 References.- 6 Manipulator Forward Dynamics.- 6.1 Introduction.- 6.2 Previous Results on Manipulator Forward Dynamics.- 6.3 The Generalized Manipulator Inertia Tensor.- 6.4 Implementation and Computational Considerations.- 6.5 Concluding Remarks.- 6.6 References.- 7 Linearized Dynamic Robot Models.- 7.1 Introduction.- 7.2 Linearization Techniques.- 7.3 Joint Space Linearized Dynamic Robot Models.- 7.4 Cartesian Space Robot Dynamic Models and their Linearization.- 7.5 Concluding Remarks.- 7.6 References.- A Recursive Lagrangian Formulation.- B On Moment Vectors and Generalized Forces.- C On Partial Differentiation.- D List of Symbols and Abbreviations.
50 citations