Global tracking for robot manipulators using a simple causal PD controller plus feedforward

Nunes, Eduardo V. L.; Hsu, Liu

doi:10.1017/s0263574709005529

Cited by 29 publications

(15 citation statements)

References 33 publications

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“…The same property is achieved via Lyapunov's direct method in [12]. Relying on the practically reasonable but theoretically restrictive assumption that the system possesses (natural) viscous friction which induces damping, the authors in [18] established global asymptotic stability. That is, the model considered is…”

Section: Introductionmentioning

confidence: 85%

Uniform global position feedback tracking control of mechanical systems without friction

Lorı́a¹

2013

2013 American Control Conference

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Abstract-We establish, as far as we know, the first proof of uniform global asymptotic stability for a mechanical system (Euler-Lagrange) in closed loop with a dynamic controller which makes use only of position measurements. The controller is fairly simple, it is reminiscent of the so-called PadenPanja controller [20] where unavailable generalized velocities are replaced by approximate differentiation (dirty derivatives). The controller has been reported previously however, only semiglobal 1 asymptotic stability has been established so far. The novelty of this paper relies in establishing a global property as well as in the method of proof, which does not follow Lyapunov's. However, the problem of finding a strict control Lyapunov function remains open.

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Section: Introductionmentioning

confidence: 85%

Uniform global position feedback tracking control of mechanical systems without friction

Lorı́a¹

2013

2013 American Control Conference

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“…Conceptually, the controller (15) may be regarded as composed of two parts: a set-point control law of the type "Proportional-Derivative with gravity cancellation" (similar, e.g., to that from [10]) which is passivity-based, and a second part which plays the role of a "feedforward" 5 :…”

Section: Discussion and Open Problemsmentioning

confidence: 99%

“…In the context of the "global tracking problem" for robot manipulators, a remarkable paper pursuing this direction is [5]. Not underestimating the authors' contribution it must nevertheless be recognized that the main result in the latter reference is stated for systems with friction, i.e., given by (2).…”

Section: Discussion and Open Problemsmentioning

confidence: 99%

“…However, subject to w = 0, we havė V ≤ 0 so V does not qualify as an input-to-state-stability Lyapunov function. Nonetheless, the authors of [5] smartly establish input-to-state stability under output feedback.…”

Section: Discussion and Open Problemsmentioning

confidence: 99%

“…At least, this is the case for lossless systems (1) since, otherwise, a simple and effective way to obtain negative terms of |q| in the bound onV , is to impose the practically reasonable, but theoretically conservative, assumption that the system possesses natural viscous friction. See, e.g., [5] in which the authors use the Lagrangian model D(q)q + C(q,q)q + Fq + g(q) = u (2) where F = F ⊤ > 0.…”

Section: Introductionmentioning

confidence: 99%

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Observers are Unnecessary for Output-Feedback Control of Lagrangian Systems

Lorı́a

2016

IEEE Trans. Automat. Contr.

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International audienceWe address and solve some long-standing yet well– documented open problems on output feedback tracking control of Euler-Lagrange systems with arbitrarily high relative degree; this includes underactuated systems. Our main contribution is to establish a theoretical foundation for the use of so-called dirty derivatives, a common " ad-hoc " replacement of unavailable state measurements such as generalized velocities, whence obviating the the use of observers for the purpose of position-feedback tracking control. Reminiscent of passivity-based control for robot manipulators, our control law is globally Lipschitz and the controller dynamics is linear. For relative-degree-two fully-actuated Lagrangian systems without dissipative forces (friction) and with bounded inertia matrix we establish uniform global asymptotic stability in closed loop. Furthermore, we show that our control approach applies to Lagrangian systems augmented by a chain of integrators (relative degree m + 2 systems). The design method, which is based on a recursive procedure in the spirit of backstep-ping control, is intuitive as it exploits structural properties such as passivity and inherent input-output stability. As a corollary, we solve an output feedback global-tracking control problem for flexible-joint robots but also for systems coupled with output-feedback linearizable actuator dynamics. In addition, we discuss remaining open problems of fairly general interest in the realm of analysis and design of robust nonlinear systems

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Observer/Controller With Global Practical Stability for Tracking in Robots Without Velocity Measurement

Driessen¹

2014

Asian Journal of Control

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In this work, a global practical stability (GPS) observer/controller is given for a revolute-jointed multiple degree of freedom robotic plant without velocity measurement and without knowledge of plant parameter values and with a globally bounded disturbance torque. For this considered plant, a global observer/controller that globally drives the combined estimation and position tracking error to a set on which the tracking error can be made arbitrarily small by adjusting parameters/gains of the observer/controller is proposed. For the above-mentioned plant, the current paper is the first GPS result for which the control torque is not an exponential function of a (filtered) tracking error. This paper is also the first global result for which the convergence to the residual set is exponential in time (Global Exponential Practical Stability). The observer update is discontinuous, however, only at isolated time instants. No sliding modes are used. Also, the torque is continuous.

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Global tracking for robot manipulators using a simple causal PD controller plus feedforward

Cited by 29 publications

References 33 publications

Uniform global position feedback tracking control of mechanical systems without friction

Uniform global position feedback tracking control of mechanical systems without friction

Observers are Unnecessary for Output-Feedback Control of Lagrangian Systems

Observer/Controller With Global Practical Stability for Tracking in Robots Without Velocity Measurement

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