Lyapunov-Based Control of Robotic Systems (Automation and by Darren M. Dawson, Aman Behal, Warren Dixon, Bin Xian

By Darren M. Dawson, Aman Behal, Warren Dixon, Bin Xian

Lyapunov-Based keep watch over of robot Systems describes nonlinear keep watch over layout options for difficulties that come up from robots required to have interaction with and manage their environments. considering that so much useful eventualities require the layout of nonlinear controllers to paintings round uncertainty and measurement-related matters, the authors use Lyapunov’s direct approach as a good software to layout and research controllers for robot systems.

After describing the evolution of real-time regulate layout structures and the linked working environments and systems, the e-book offers a bunch of normal keep watch over layout instruments for robot structures utilizing a typical Lyapunov-based framework. It then discusses numerous difficulties in visible servoing keep an eye on, together with the layout of homography-based visible servo keep an eye on tools and the vintage constitution from movement challenge. The booklet additionally offers with the problems of direction making plans and keep an eye on for manipulator palms and wheeled cellular robots. With a spotlight at the rising learn region of human computer interplay, the ultimate bankruptcy illustrates the layout of regulate schemes in keeping with passivity such that the laptop is a web strength sink.

Including a lot of the authors’ personal examine paintings in controls and robotics, this publication enables an figuring out of the applying of Lyapunov-based keep watch over layout innovations to up-and-coming difficulties in robotics.

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This technique was only applicable to the case where the motion of the arm was restricted to a plane orthogonal to the optical axis of the camera. However, the result in [57] demonstrated conclusively that there is a large difference in curvature measurements obtained from indirect cable measurements as compared to a vision-based strategy, and hence, the information obtained from ad hoc indirect shape measurement techniques is indeed questionable. 4 addresses this issue through a visual servo control approach.

70) ¡ ¢ ¡ ¢ 0 where σ (Vˆ T ξ) ≡ dσ V T ξ /d V T ξ |V T ξ=Vˆ T ξ , and O(Vˆ T ξ)2 denotes the higher order terms. 71) 0 where σ ˆ , σ (Vˆ T ξ). 73) where k·kF is the Frobenius norm of a matrix, and tr (·) is the trace of a matrix. 8 The estimates for the NN weights, W bounded using a smooth projection algorithm (see [21]). 9 The typical choice of activation function is the sigmoid function 1 , σ(ξ) = 1 + eκξ where kσk < 1 and kσk ˙ ≤ σn, and σ n ∈ R is a known positive constant. © 2010 by Taylor and Francis Group, LLC 26 2.

106), if r(t) is regulated then eN (t) is regulated, and hence, the sub-task control can also be achieved. 105) also provides motivation to regulate r(t) in order to regulate e(t). 107) M r˙ = −Vm r + Y φ − τ © 2010 by Taylor and Francis Group, LLC 32 2. , mass, inertia, friction coefficients). 109) where K ∈ Rn×n is a constant, positive definite, diagonal gain matrix. 110) M r˙ = −Vm r − J T e − Kr. 109) guarantees global exponential task-space and sub-task tracking in the sense that both signals e(t) and eN (t) are bounded by an exponential envelope.

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