Controllability and Observability of an -Link Planar Robot with a Single Actuator Having Different Actuator–Sensor Configurations

Liu, Yannian; Xin, Xin

doi:10.1109/tac.2015.2460393

Cited by 29 publications

(32 citation statements)

References 13 publications

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“…If

(||, {normal Ψ}_{3} (λ)) \neq 0

, the controllability of the original system is equivalent to that of the second system in Figure . According to , these two systems are linearly controllable. If

(||, {normal Ψ}_{2} (λ)) \neq 0

, the controllability of the original system is equivalent to that of the third system in Figure .…”

Section: Discussionmentioning

confidence: 99%

“…Thus, for any λ >0, if any of Ψ 1 ( λ ),Ψ 2 ( λ ), and Ψ 3 ( λ ) is non‐singular, the original robot is linearly controllable. As the dual version of controllability, the results for observability can be obtained similarly. Liu and Xin investigated the linear controllability and observability of an n ‐link robot with a single actuator. It mentioned that a challenging problem is the linear controllability and observability of an n ‐link planar robot having multiple actuators and encoders with different configurations.…”

Section: Discussionmentioning

confidence: 99%

“…/j ¤ 0, the controllability of the original system is equivalent to that of the second system in Figure 3. According to [19], these two systems are linearly controllable. If j‰ 2 .…”

Section: Discussionmentioning

confidence: 99%

“…The link angle θ i is the angle between link i and the positive y ‐axis. Its equation of motion is formulated as follows, which is obtained from :

M (θ) \overset{θ}{true} + C (θ, \overset{θ}{true}) \overset{θ}{true} + G (θ) = τ = B u,

where

θ = {[\begin{matrix} array θ_{1}, & array θ_{2}, & array \dots, & array θ_{n} \end{matrix}]}^{T} \in {double-struckR}^{n}

;

M (θ) \in {double-struckR}^{n \times n}

is the symmetric positive definite inertia matrix with

{([], M (θ))}_{i j} = α_{i j} \cos (θ_{j} - θ_{i})

; and

C (θ, \overset{θ}{true})

is an n × n matrix defined as

{([], C (θ, \overset{θ}{true}))}_{i j} = - α_{i j} {\overset{θ}{true}}_{j} \sin (θ_{j} - θ_{i})

;

G (θ) \in {double-struckR}^{n}

with

{([], G (θ))}_{i} = - β_{i} \sin θ_{i}

.…”

Section: Model Of N‐link Robot and Preliminariesmentioning

confidence: 99%

“…The link angle Â i is the angle between link i and the positive y-axis. Its equation of motion is formulated as follows, which is obtained from [19]:…”

Section: Model Of N-link Robotmentioning

confidence: 99%

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Controllability and observability of ann‐link robot with multiple active links

Hao

Duan

Wen

2017

Intl J Robust & Nonlinear

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Summary This paper considers an n‐link planar robot moving in the vertical plane with multiple active links. The controllability and observability of the robot around the upright equilibrium point, which are important for the existence of an output‐feedback controller, are investigated in detail. Specific properties of the mechanical parameters are extracted to demonstrate that when there are adjacent active links, the robot is strongly structurally controllable and observable around the upright equilibrium point. When the active links are not adjacent to each other, a necessary and sufficient condition is established to ensure the linear controllability and observability. Finally, the theoretical results are illustrated via several practical examples. Copyright © 2017 John Wiley & Sons, Ltd.

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“…If

(||, {normal Ψ}_{3} (λ)) \neq 0

, the controllability of the original system is equivalent to that of the second system in Figure . According to , these two systems are linearly controllable. If

(||, {normal Ψ}_{2} (λ)) \neq 0

, the controllability of the original system is equivalent to that of the third system in Figure .…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…/j ¤ 0, the controllability of the original system is equivalent to that of the second system in Figure 3. According to [19], these two systems are linearly controllable. If j‰ 2 .…”

Section: Discussionmentioning

confidence: 99%

“…The link angle θ i is the angle between link i and the positive y ‐axis. Its equation of motion is formulated as follows, which is obtained from :

M (θ) \overset{θ}{true} + C (θ, \overset{θ}{true}) \overset{θ}{true} + G (θ) = τ = B u,

where

θ = {[\begin{matrix} array θ_{1}, & array θ_{2}, & array \dots, & array θ_{n} \end{matrix}]}^{T} \in {double-struckR}^{n}

;

M (θ) \in {double-struckR}^{n \times n}

is the symmetric positive definite inertia matrix with

{([], M (θ))}_{i j} = α_{i j} \cos (θ_{j} - θ_{i})

; and

C (θ, \overset{θ}{true})

is an n × n matrix defined as

{([], C (θ, \overset{θ}{true}))}_{i j} = - α_{i j} {\overset{θ}{true}}_{j} \sin (θ_{j} - θ_{i})

;

G (θ) \in {double-struckR}^{n}

with

{([], G (θ))}_{i} = - β_{i} \sin θ_{i}

.…”

Section: Model Of N‐link Robot and Preliminariesmentioning

confidence: 99%

“…The link angle Â i is the angle between link i and the positive y-axis. Its equation of motion is formulated as follows, which is obtained from [19]:…”

Section: Model Of N-link Robotmentioning

confidence: 99%

See 3 more Smart Citations