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## Task-Space and Null-Space Control Design for Robotic-Assisted Minimally Invasive Surgery

### Citations

459 |
A unified approach for motion and force control of robot manipulators: The operational space formulation
- Khatib
- 1987
(Show Context)
Citation Context ...ery time; 9) Tele-surgery; 10) Training, learning and mentoring using virtual models; This paper proposes a systematic control design for robotized MIS, based on operational and null space techniques =-=[9]-=- linked to AOBs [4], [5]. It extends the work of [10] through haptic feedback, eliminating gradient-based functions from the control design. Section II introduces the experimental setup and the D2M2 k... |

212 |
Computer controlled systems, theory and design
- Åström, Wittenmark
- 1990
(Show Context)
Citation Context ... methods, though. 4The symbol ˆ means estimate. 5The analysis is done for each Cartesian dimension. In compact form,{ ẋ(t) = Ax(t)+Bu(t−Td) y(t) = x1(t) . (17) Discretizing (14) with sampling time h =-=[1]-=-, the equivalent discrete time system is{ xr,k =Φrxr,k−1+Γruk−1 yk =Crxr,k , (18) with Td = (d−1)h+ τ′, (19) 0< τ′ ≤ h, (20) xr,k = [ xk uk−d · · · uk−2 uk−1 ]T , (21) Φr = Φ1 Γ1 Γ0 · · · 0 0 ... |

11 |
Kalman Techniques for Intelligent Control Systems: Theory and Robotic Experiments
- Cortesão
- 2003
(Show Context)
Citation Context ...urgery; 10) Training, learning and mentoring using virtual models; This paper proposes a systematic control design for robotized MIS, based on operational and null space techniques [9] linked to AOBs =-=[4]-=-, [5]. It extends the work of [10] through haptic feedback, eliminating gradient-based functions from the control design. Section II introduces the experimental setup and the D2M2 kinematic and dynami... |

5 |
Stochastic Processes and Filtering Theory, volume 64 ofMathematics in Science and Engineering
- Jazwinsky
- 1970
(Show Context)
Citation Context ...ŷk =Ca ([ Φr−ΓrLr 0 0 1 ][ x̂r,k−1 p̂k−1 ] + [ Γr 0 ] rk−1 ) (33) and Ca = [ Cr 0 ] . (34) The Kalman gain Kk reflects the uncertainty associated to each state, which is a function of ξk and ηk [3], =-=[7]-=-. It is given by Kk = P1kCTa [CaP1kC T a +Rk] −1 , (35) with P1k =ΦnPk−1ΦTn +Qk (36) and Pk = P1k−KkCaP1k. (37) Φn is the augmented open loop matrix, Φn = [ Φr Γr 0 1 ] . (38) The system noise matrix ... |

3 | Real-time adaptive control for haptic telemanipulation with kalman active observers
- Cortesão, Park, et al.
(Show Context)
Citation Context ...y; 10) Training, learning and mentoring using virtual models; This paper proposes a systematic control design for robotized MIS, based on operational and null space techniques [9] linked to AOBs [4], =-=[5]-=-. It extends the work of [10] through haptic feedback, eliminating gradient-based functions from the control design. Section II introduces the experimental setup and the D2M2 kinematic and dynamic mod... |

3 | Haptic control design for robotic-assisted minimally invasive surgery - Cortesão, Zarrad, et al. - 2006 |

3 | Dynamic task posture decoupling for minimally invasive surgery motions
- Michelin, Poignet, et al.
- 2004
(Show Context)
Citation Context ...d mentoring using virtual models; This paper proposes a systematic control design for robotized MIS, based on operational and null space techniques [9] linked to AOBs [4], [5]. It extends the work of =-=[10]-=- through haptic feedback, eliminating gradient-based functions from the control design. Section II introduces the experimental setup and the D2M2 kinematic and dynamic models. Task space control is ad... |

1 |
Synthèse de la comande dynamique d’un téléopérateur redondant. RAIRO
- Liégeois, Meyer, et al.
- 1975
(Show Context)
Citation Context ...refore, J+t represents its pseudo-inverse. In the experiments, the dynamically consistent pseudo-inverse has been used, i.e. J+t =M −1JTt (JtM −1JTt ) −1, (9) which minimizes the robot kinetic energy =-=[2]-=-, [8]. One advantage of truncated Jacobian solutions for robots that are not intrinsically redundant is the possibility to utilize the null space to optimize another objective function, very useful in... |