design and modeling of cable- driven parallel robots ... · pdf filesince cables cannot push...

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Design and Modeling of Cable-driven Parallel Robots: State of the Art and Open Issues

1Original presentation by Stéphane CARO

Antoine MARTIN – Project NUSANTARA – 24 november2016

Summary

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1. Introduction

2. Open Problems

1. Direct Geometrico-Static Problem

2. Workspace Analysis

3. Tension Distribution

4. Stiffness Modelling

5. Design of CDPRs

6. Design and Reconfigurability of RCDPRs

3. Conclusions

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Introduction

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Advantages Drawbacks

High payload Cables in tension

Large workspace Collisions

Low inertia, high velocities and accelerations

Vibrations / instability

Modularity and flexibility

Solving the direct geometric problem

Simple

Cable-driven parallel robots:


Introduction

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2.5 US Patent 6826452 2.6 NIST, ROBOCRANE

Cable-driven parallel robots: applications

Displacement of heavy payloads in large spaces

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Introduction

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ANR COGIRO prototype

http://www.lirmm.fr/cogiro/

Displacement of heavy payloads in large spaces

CoGiRo


Introduction

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Displacement of light payloads in large spaces

Skycam LAR (Large Adpative Reflector) - Canada

http://www.lirmm.fr/cogiro/

https://youtu.be/-CmjXwXEZJA

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Introduction

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Ultra High-Speed Robot FALCONKawamura et al., 1995

Max.: 43G, 13m/s

Displacement of objects with high velocities


IPANEMA Robot DUISBURG


Introduction

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Université Laval, Québec, Canada

(Cardou et al., 2014)


Haptic device

../../../../Biblio/Videos-Photos/CableDrivenParallelRobots/IPAnema -- a high dynamic parallel cable robot.avi

../../../../Biblio/Videos-Photos/CableDrivenParallelRobots/Robot_Tobias_BRUCKMANN_video-2014-08-26-14-07-28.mp4

../../../../Biblio/Videos-Photos/CableDrivenParallelRobots/Proto_Philippe_CARDOU/CARDOU_haptic-feedback-cable-driven-parallel-robot.mp4

https://www.youtube.com/watch?v=w3yh-Qbi1D0

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Introduction

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Rescue crane (Merlet and Daney, 2010)

Systèmes d’aide à la personne, de réhabilitation ou aisément transportable et déployable pour des opérations

de secours en état d’urgence


Introduction

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ACROBOT

Cable-driven parallel robots: IRT JV proto 1

https://www.youtube.com/watch?v=wG8nE-wBhoE&feature=youtu.be

../../../../Biblio/Videos-Photos/CableDrivenParallelRobots/CAROCA/acrobot.MOV

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Introduction

13 CAROCA prototype



Introduction

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Reconfigurable CDPR


➢ Gagliardini, L., Caro, S., Gouttefarde, and M., Girin, A.„ 2016, “Discrete Reconfiguration Planning for Cable-Driven Parallel Robots”,Mechanism and Machine Theory, Vol. 100, pp. 313 - 337.

../../../../Biblio/Videos-Photos/CableDrivenParallelRobots/CAROCA/CAROCA_proto/CAROCA_Prototype_Movies/160420_CAROCA_Prototype_Movie1_v2_ordi.wmv

../../../../Biblio/Videos-Photos/CableDrivenParallelRobots/CAROCA/CAROCA_proto/CAROCA_Prototype_Movies/160420_CAROCA_Prototype_Movie1_v2_ordi.wmv

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Inverse Geometric Model

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• The inverse geometric model of a CDPR is quite simple. Given the pose of the moving platform, cable lengths are defined through linear equations.

• Cables are usually represented by massless linear segments.

𝒍𝒊 𝒊𝒕𝒉 cable vector

𝒅𝒊 𝒊𝒕𝒉 cable unit vector

𝒂𝒊𝒃 Exit point location for the 𝒊𝒕𝒉 cable

𝒃𝒊𝒃 Moving platform connection point location for the 𝒊𝒕𝒉 cable

𝒕 Cartesian coordinates of the moving platform CoM𝑹 Orientation matrix of the moving platform

➢ R.G. Roberts, T. Graham, and T. Lippitt. On the inverse kinematics, statics, and fault tolerance of cable-suspended robots. J. of Robotic Syst.,15(10):581–597, Oct. 1998.


Static Equilibrium

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• The static equilibrium of the moving platform is described by linear equations

• However, cable tensions are constrained to be positive Semi-Algebraic Problem

𝑾 Wrench matrix

𝑾† Pseudo-inverse of the wrench matrix𝒘𝑒 External wrench𝝉 Cable tension vector𝒏 Null space of the wrench matrix𝝀 Vector of the null space multipliers


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Antoine MARTIN – Project NUSANTARA – 24 november2016 19

Direct Geometrico-Static Problem


Direct Geometrico-Static Problem #1

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▪ The direct geometrico-static problem aims at defining the poses of a CDPR moving platform and the cable tensions required to assure its static equilibrium assuming that the lengths of the cables are known.

▪ Due to the unilateral nature of the kinematic constraints, cables can only pull the platform and not push it.

▪ The characteristics of the direct geometrico-static problem depend on:

▪ The number of tensed cables and the DoF of the moving platform (the number of tensed cables may change according to the moving platform pose).

▪ The cable model

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▪ CDPRs modeled with linear cables can be classified into:

▪ Under-Constrained CDPRs: 𝒎 < 𝒏

▪ Fully Constrained CDPRs: 𝒎 = 𝒏

▪ Over-Constrained CDPRs: 𝒎 > 𝒏

▪ The solutions of the corresponding univariate polynomial are:

Number of Cables (m) Number of equations Number of Complex Solutions

6 (𝑚 = 𝑛) 6 Geometric 40

5 (𝑚 < 𝑛) 11 = 5 Geometric + 6 Static 128



➢ G. Abbasnejad and M. Carricato. Direct geometrico-static problem of underconstrained cable-driven parallel robots. IEEE Trans. on Robotics,31(2):468–478, Apr. 2015.

➢ M. Carricato and G. Abbasnejad. Direct geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables. In Cable-Driven Parallel Robots, volume 12 of Mechanisms and Machine Science, 269–285. Springer, 2013.

➢ M. Carricato. Direct geometrico-static problem of underconstrained cable-driven parallel robots with three cables. ASME J. of Mechanisms andRobotics, 5(3), June 2013.



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▪ Over-constrained CDPR (𝒎>𝒏) admit an infinite number of solutions in terms of cable tension distribution

▪ According to the architecture of the CDPR, some cables may be slack in certain moving platform poses.

▪ It is necessary to verify the presence of slack cables and to check whether the solutions to the direct-geometricostatic problem are stable or not

▪ The direct-geometrico static problem of over-constrained CDPRs can be solved numerically or by means of interval analysis.

➢ A. Berti, J.-P. Merlet, and M. Carricato. Workspace analysis of redundant cable-suspended parallel robots. In Cable-Driven Parallel Robots,volume 32 of Mechanisms and Machine Science, 41–53. Springer, 2015

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▪ The sagging model is more accurate but the system of equations is not algebraic

𝑬 Young modulus𝑨𝟎 Cable section𝝀𝟎 Elastic cable coefficient

𝒙𝒊 , 𝒛𝒊 Coordinates of the 𝒊𝒕𝒉 exit point𝑭𝒙,𝒊, 𝑭𝒛,𝒊 Cable force components exerted on the platform by the 𝒊𝒕𝒉 cable

𝒍𝟎,𝒊 Length of the unstrained 𝒊𝒕𝒉 cable

➢ M. Irvine. Cable structures. Dover Publications, June 1992.



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▪ Both the direct and the inverse geometrico-static problems of a CDPR with sagging cables can be solved numerically

▪ The problem can be solved by means of interval analysis, supposing that only six cables are tensed

▪ The problem admits several solutions, but some of them may not lead to a static equilibrium of the moving-platform

➢ J.-P. Merlet and D. Daney. Legs interference checking of parallel robots over a given workspace or trajectory. In Proc. of the IEEE Int. Conf. onRobotics and Automation (ICRA 2006), 757–762, Orlando, FL, May 2006.

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▪ The direct geometrico-static problem can be solved using different methods, according to the ratio between 𝑚 and 𝑛 and the cable model. Existing methods are complex and time consuming. The solutions have to be analysed in order to verify whether they lead to a static equilibrium of the moving platform or not

▪ Open questions:

▪ Is it possible to compute all the moving platform poses which assure its static equilibrium for a CDPR with sagging cables?

▪ Is it possible to develop a method to compute the feasible solutions of the Direct Geometrico-Static in real time ?


Tension Distribution

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▪ Over-constrained CDPRs admit an infinite set of feasible solutions

▪ Cable tensions can be adjusted in order to minimize the energy consumption

of the CDPR (𝐦𝐢𝐧 𝝉 𝟐) or to prevent cables from becoming slack (𝐦𝐢𝐧 𝒍 𝟐)

▪ Cable tensions in CDPRs with massless cables can be minimised by using the null space of the wrench matrix

➢ Borgstrom, P.H et al. (2009): Rapid Computation of Optimally Safe Tension Distributions for Parallel Cable-Driven Robots. In: IEEE Trans.Robot. 25 (6), 1271–1281.

➢ Borgstrom, Per Henrik et al. (2009): NIMS-PL A Cable-Driven Robot With Self-Calibration Capabilities. In: IEEE Transactions on Robotics 25(5), 1005-1015.

➢ Taghirad, Hamid Reza; Bedoustani, Yousef Babazadeh (2011): An Analytic-Iterative Redundancy Resolution Scheme for Cable-DrivenRedundant Parallel Manipulators. In: IEEE Transactions on Robotics 27 (6), 1137–1143.



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▪ Cable tension distribution can be computed by means of alternative methods based on the analysis of two cable tension spaces:

▪ The space of the admissible cable tensions.

▪ The space of the cable tensions which assure the static equilibrium of the moving platform.

𝜏1𝜏2

𝜏3

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▪ Several methods have been proposed for CDPRs with linear cables :

▪ Barycentre Approach

▪ Closed-Form Method

▪ Corner Projection

▪ Puncture Method

Barycentre Approach Puncture MethodClosed-Form Method

➢ Mikelsons, Lars; Bruckmann, Tobias; Hiller, Manfred; Schramm, Dieter (2008): A real-time capable force calculation algorithm for redundanttendon-based parallel manipulators. In: 2008 IEEE International Conference on Robotics and Automation: IEEE, 3869–3874.

➢ Pott, Andreas; Bruckmann, Tobias; Mikelsons, Lars (2009): Closed-form Force Distribution for Parallel Wire Robots. In: Andrés Kecskeméthyund Andreas Müller (Hg.): Computational Kinematics. Berlin, Heidelberg: Springer Berlin Heidelberg, 25–34.



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▪ Tension distribution in CDPRs with sagging cables can be performed by means of constraint optimization techniques

▪ The optimization problem aims at minimising the cable tensions while satisfying the kinematic and the static equilibrium constraints of the moving platform.

Static equilibrium constraints:

Geometric constraints:

Objective functions:

Optimization problem:

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▪ Several tension distribution techniques have been defined for CDPRs with linear cables. Each of them has several advantages and drawbacks in terms of tension minimization, solution continuity and time consumption

▪ Is it possible to implement a tension distribution method for CDPRs with linear cables that provides feasible continuous solutions in real time, while minimising cable tensions?


Workspace Analysis

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Workspace Analysis

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▪ Since cables cannot push the moving platform, the static and dynamic equilibrium of the CDPR should be verified.

▪ The CDPR workspace, based on the moving platform static equilibrium, is defined as « Wrench Feasible Workspace » (WFW).

Static equilibrium:

Constraints:

WFW:

➢ P. Bosscher, A.T. Riechel, and I. Ebert-Uphoff. Wrench-feasible workspace generation for cabledriven robots. IEEE Trans. on Robotics,22(5):890–902, Oct. 2006.

➢ S. Bouchard, C. M. Gosselin, and B. Moore. On the ability of a cable-driven robot to generate a prescribed set of wrenches. In Proc. of the ASMEInt. Design Eng. Tech. Conf. & Comput. And Inform. in Eng. Conf. (IDETC/CIE 2008), 47–58, Brooklyn, NY, Aug. 2008.


Workspace Analysis

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▪ The WFW is analysed by comparing the Available Wrench Set (AWS), , and the Required Wrench Set (RWS), .

▪ The AWS is a zonotope is an affine space generated by the linear mapping of the Available Cable Tension Set (ACTS), , into the wrench space.

▪ The wrench feasibility can be analysed measuring the distances between the vertices of the RWS and the facets of the AWS.

𝜏1

𝜏3

𝜏2

Wrench feasibility:

➢ M. Gouttefarde, D. Daney, and J.-P. Merlet. Interval-analysis-based determination of the wrench feasible workspace of parallel cable-drivenrobots. IEEE Trans. on Robotics, 27(1):1–13, Feb. 2011.

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Wrench Feasible Workspace (WFW)

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𝑤𝑒 = Required Wrench set

F= Available Wrench

F + 𝑤𝑒= 0System to solve:

An index measuring the degree of inclusion or exclusion of

the required wrench set inside the available wrench set:

the signed distance from each vertex of the required

wrench set to each face of the available wrench set.

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s = + (Positive)

s = - (Negative)

s = 0

Degree of

Inclusion

𝑤𝑒

F

𝑤𝑒 F 𝑤𝑒 F

➢ Cruz Ruiz, A. L., Caro, S., Cardou, P. and Guay, F., 2015, “ARACHNIS : Analysis of Robots Actuated by Cables with Handy and Neat InterfaceSoftware”, Cable-Driven Parallel Robots, Mechanisms and Machine Science, Volume 32, pp. 293–305.

Capacity MarginS

tép

ha

ne

CA

RO

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How to compute these sets?

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Wrench Matrix Available Tension Set Required Wrench Set

Available Wrench Set (F)

n (DOFS) × m (number cables) m × 1 n × 1

W= 𝒄𝟏 … 𝒄𝒎

1

𝑟𝒓𝟏 × 𝒄𝟏 …

1

𝑟𝒓𝒎 × 𝒄𝒎

Ԧ𝒕 =

𝑡1⋮𝑡𝑚

𝑾Ԧ𝒕 + 𝒘𝒆= 𝟎𝒏

𝑤𝑒

F

Sté

ph

an

e C

AR

O

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Tensi

on s

pace

(m-d

imensi

onal Space)

Available Tension Set (Ԧ𝒕)

Wre

nch s

pace

(n-d

imensi

onal Space)

Available Wrench Set (F)

n-1 dimensional facets!

Required Wrench Set (𝒘𝒆)

The Polytopes of a CDPR

𝑾Ԧ𝒕 + 𝒘𝒆= 𝟎𝒏

𝐓𝐧−𝟏,𝐤,𝐥=ቄ

ቅ

Ԧ𝐭 ∈ Rm: 𝑡𝑖 ≤ 𝑡𝑖 ≤ 𝑡𝑖 , 𝑖 ∈ Tk, 𝑡𝑖 = 𝑡𝑖, 𝑖 ∈ Lk,l, 𝑡𝑖 = 𝑡𝑖 ,

𝑖 ∈ Uk,l

𝐅𝐤,𝐥= 𝐰 ∈ Rn: 𝐰 = −𝐖Ԧ𝐭, Ԧ𝐭 ϵ Tn−1,k,l

Facet Representation Vertex Representation(𝒂𝒌, 𝑏𝑘 )

𝐅𝐤,𝐥= 𝐰 ∈ Rn: 𝒂𝒌𝑇𝐰 ≤ 𝑏𝑘 , 𝑘 = 1… . 𝑞 𝑒𝑥: 𝐹𝑥= 𝐹𝑥𝑚𝑖𝑛 𝐹𝑥𝑚𝑎𝑥

Where k is a family , and l a facet of each family

Sté

ph

an

e C

AR

O

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Computation of Index “s” (Minimum Degree of Constraint Satisfaction for each pose)

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Distance from vertex r (Required Wrench

Set) to face l (Available Wrench Set):

Minimum distance:

Where h is the total number of

vertices, and q the total number of

faces

Sté

ph

an

e C

AR

O


Workspace Analysis

➢ Cruz Ruiz, A. L., Caro, S., Cardou, P. and Guay, F., 2015, “ARACHNIS : Analysis of Robots Actuated by Cables with Handy and Neat InterfaceSoftware”, Cable-Driven Parallel Robots, Mechanisms and Machine Science, Volume 32, pp. 293–305.40

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Workspace Analysis

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Workspace Analysis

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Workspace Analysis

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Workspace Analysis

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Workspace Analysis

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▪ The CDPR workspace, based on the moving platform kinematic constraints, is defined as « Twist Feasible Workspace » (TFW).

➢ Gagliardini, L., Caro, S., Gouttefarde, M. and Girin, A., “Dimensioning of Cable-Driven Parallel Robot Actuators, Gearboxes and WinchesAccording to The Velocity Feasible Workspace”, IEEE International Conference on Automation Science and Engineering (CASE 2015).Gothenburg, Sweden, Aug., 2015

Kinematic constraints:

Constraints:

TFW :

Twist feasibility:


Workspace Analysis

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▪ The CDPR workspace, based on the moving platform dynamic equilibrium, is defined as « Dynamic Feasible Workspace » (DFW).

Dynamic equilibrium:

Constraints:

DFW :

Dynamic feasibility:

➢ G. Barrette and C.M. Gosselin. Determination of the dynamic workspace of cable-driven planar parallel mechanisms. ASME J. of Mech. Design,127(2):242–248, 2005.

➢ Cruz Ruiz, A. L., Caro, S., Cardou, P. and Guay, F., 2015, “ARACHNIS : Analysis of Robots Actuated by Cables with Handy and Neat InterfaceSoftware”, Cable-Driven Parallel Robots, Mechanisms and Machine Science, Volume 32, pp. 293–305.

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Workspace Analysis

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▪ The wrench feasibility analysis leads to interesting results. However, the WFW can be computed only by discretizing the prescribed workspace of the CDPR or by means of interval analysis.

▪ Is it possible to develop an analytical tool to compute the exact boundaries of the WFW?

▪ The IDFW supposes that the twist of the moving platform is constant.

▪ Is it possible to analyse the dynamic feasibility of a CDPR supposing that the moving platform can assume a range of user-defined twists?

▪ The workspace of CDPRs has been formally defined for linear cable models.

▪ How can we represent mathematically the wrench feasibility conditions for CDPRs with sagging cables?


Stiffness modelling

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Stiffness Modelling #1

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▪ The elasto-static model of CDPRs are defined according to the cable model describing the CDPRs.

▪ An accurate geometric model of the CDPR may include the influence of pulleys in the platform pose.

Reference Cable Mass Pulleys Cable Model

Roberts et al (1998) Linear

Bruckmann et al (2010) X Linear

Kozak et al (2006) X Sagging

Gouttefarde et al (2014)X X Sagging


➢ T. Bruckmann. Auslegung und Betrieb redundanter paralleler Seilroboter. PhD thesis, Universität Duisburg-Essen, Sept. 2010.

➢ K. Kozak, Qian Zhou, and Jinsong Wang. Static analysis of cable-driven manipulators with non-negligible cable mass. IEEE Trans. on Robotics,22(3):425–433, June 2006.

➢ M. Gouttefarde, D.Q. Nguyen, and C. Baradat. Advances in Robot Kinematics, chapter Kinetostatic Analysis of Cable-Driven Parallel Robotswith Consideration of Sagging and Pulleys, 213– 221. Springer, 2014.



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▪ According to the geometric model of the CDPR, several elasto-static models have been proposed in the literature. These models are valid for small displacements of the moving-platform.

Reference Cable Mass Pulleys Task Space Cable Model

Bezhadipour et al. (2005) 2T1R Linear

Surdilovic et al (2013) X 3T Linear

Arsenault et al (2013) X 3T Sagging

Gouttefarde et al (2014) X 3T3R Sagging

Gagliardini et al (2015) X X 3T3R Sagging

➢ S. Behzadipour and A. Khajepour. Stiffness of cable-based parallel manipulators with application to stability analysis. ASME J. of Mech. Design,128(1):303–310, Apr. 2005.

➢ D. Surdilovic, J. Radojicic, and J. Krüger. Geometric stiffness analysis ofwire robots: A mechanical approach. In Cable-Driven Parallel Robots,volume 12 of Mechanisms and Machine Science, 389–404. Springer, 2013.

➢ M. Arsenault. Workspace and stiffness analysis of a three-degree-of-freedom spatial cable suspended parallel mechanism while consideringcable mass. Mechanism and Machine Theory, 66:1–13, Aug. 2013.

➢ M. Gouttefarde, D.Q. Nguyen, and C. Baradat. Advances in Robot Kinematics, chapter Kinetostatic Analysis of Cable-Driven Parallel Robotswith Consideration of Sagging and Pulleys, 213– 221. Springer, 2014.

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▪ The elasto-static models based on the linear cable model are computed according to the following differential form:

Active Stiffness Matrix

Passive Stiffness Matrix

K Cartesian Stiffness matrix𝜹𝒘𝒆 Small variations in the external wrench𝜹𝒑 Small variations in the moving platform pose𝜹𝒕 Small variations in the moving platform position𝜹𝒓 Small variations in the moving platform orientation

➢ S. Behzadipour and A. Khajepour. Stiffness of cable-based parallel manipulators with application to stability analysis. ASME J. of Mech. Design,128(1):303–310, Apr. 2005.



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▪ The elasto-static models based on the sagging cable model are computed referring to the following moving platform static equilibrium equation:

𝑾𝒊 Force projection matrix𝑹𝒊 Cable reference frame orientation


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▪ Simulation of a suspended CDPR with sagging cables:




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▪ Simulation of a fully constrained CDPR with sagging cables:

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▪ The elasto-static models of CDPRs with sagging cables have been computed following different procedures.

▪ Are those developed elasto-static models of CDPRs with sagging cables equivalent?

▪ The effect of pulleys on the elasto-static modelling of CDPRs with sagging cables has not be taken into account.

▪ Is it possible to express the elasto-static model of CDPR with sagging cables while considering the pulleys?

▪ Few research work focuses on the analysis of the elasto-static model of CDPR with large moving platform displacements.

▪ Which will be the best elasto-static model for large moving platform displacements?


Design

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Design of CDPRs #1

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▪ The design of CDPRs intends to dimension the CDPR components and define its geometry.

▪ Several CDPR designs rely on the intuition of their designers.

➢ S. Kawamura, W. Choe, S. Tanaka, and S.R. Pandian. Development of an ultrahigh speed robot FALCON using wire driven system. In Proc. ofthe IEEE Int. Conf. on Robotics and Automation (ICRA 1995), volume 1, pages 215–220, Nagoya, Japan, May 1995

➢ P. Lafourcade. Etude des manipulateurs parallèles à câbles, conception d’une suspension active pour soufflerie. PhD thesis, Thèse de DocteurIngénieur ENSAE, 2004.


Design of CDPRs #2

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▪ In 2004, one of the preliminary trajectory-based design approaches has been proposed by Pusey et al. The design problem is formulated as an optimisation problem aiming at improving the size of the CDPR workspace.

▪ In 2008, Gouttefarde et al. proposed an optimal design strategy based on interval analysis.

Basic definitions of the Interval Analysis:

Application to the Wrench matrix:

➢ J. Pusey, A. Fattah, S. Agrawal, and E. Messina. Design and workspace analysis of a 6-6 cable-suspended parallel robot. Mechanism andMachine Theory, 39(7):761–778, July 2004.

➢ M. Gouttefarde, S. Krut, O Company, F. Pierrot, and N. Ramdani. Advances in Robot Kinematics, chapter On the Design of Fully ConstrainedParallel Cable-Driven Robots, pages 71–78. Springer, 2008.

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Design of CDPRs #5

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▪ Optimal design of a CDPR based on the dimensioning of the motors, the winches and the gearboxes. The optimization aims at maximising the size of the WFW and the TWF.

Problem definition:

Optimal solution:

➢ L. Gagliardini, S. Caro, and M. Gouttefarde. Dimensioning of cable-driven parallel robot actuators, gearboxes and winches according to thetwist feasible workspace. In Proc. of the IEEE Int. Conf. on Automation Science and Engineering (CASE 2015), 99–105, Gothenburg, Sweden,Aug. 2015.


Design of CDPRs #6

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▪ Several CDPR design strategy have been proposed in the literature. Each strategy focuses on one or more components of the CDPRs

▪ Is it possible to define a design strategy for CDPRs which aims at dimensioning all the components of a CDPR?

▪ Being the design problem formulated as an optimization problem, several optimisation algorithms have been tested?

▪ Which is the best optimisation algorithm to be used in order to solve the optimization problems associated to the design of CDPRs?

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Reconfigurability


Design and Reconfigurability of RCDPRs #1

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▪ Reconfiguration of CDPRs mostly focuses on the displacement of cable exit points.

▪ The main classification of RCDPRs is between:

Discrete ReconfigurationsContinuous Reconfigurations

➢ L. Blanchet. Contribution à la modélisation de robots à câbles pour leur commande et leur conception. PhD thesis, Université Nice Sophia-Antipolis, Mai 2015.

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▪ In continuous RCDPRs, exit points can assume a continuous set of possible locations.

▪ Planar RCDPR can be modelled and designed through an analytical optimisation.

▪ Spatial RCDPRs can be designed through a local numerical optimisation.

➢ G. Rosati, P. Gallina, and S. Masiero. Design, implementation and clinical test of a wire-based robot for neurorehabilitation. IEEE Trans. onNeural Syst. and Rehabilitation Eng., 15(4):560–569, Dec. 2007.

➢ X. Zhou, S. Jun, and V. Krovi. Tension distribution shaping via reconfigurable attachment in planar mobile cable robots. Robotica, 32(2):245–256, Mar. 2013.



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▪ Optimal design of a RCDPRs

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Wenger, P. and Girin, A., “A Reconfigurable Cable-Driven Parallel Robot for Sandblasting andPainting of Large Structures”, Second International Conference on Cable-Driven Parallel Robots (CableCon 2014), Duisburg, Germany, Aug.,2014

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▪ In discrete RCDPRs, exit points can be located at a possibly large but finite number of locations.

14400 configurations possibles

1186 selected configurations

➢ Gagliardini, L., Caro, S., Gouttefarde, M. and Girin, A., “A Reconfiguration Strategy for Reconfigurable Cable-Driven Parallel Robots”, IEEEInternational Conference on Robotics and Automation (ICRA 2015). Seattle, Washington, May, 2015

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Girin, A. and Yvan, P. , “Brevet FR 1457672”,Nantes, 7th, August, 2014 [Submitted].



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▪ Validation of the reconfiguration strategy (external parts)

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Girin, A. , “An Optimal Task Based Reconfiguration Strategy for Cable-Driven Parallel Robots”,Machines and Mechanisms, Elsevier [Submitted].


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▪ Validation of the reconfiguration strategy (internal parts)

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Girin, A. , “An Optimal Task Based Reconfiguration Strategy for Cable-Driven Parallel Robots”,Machines and Mechanisms, Elsevier [Submitted].




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▪ The design strategies based on analytical optimizations are limited to planar continuous RCDPRs.

▪ Can we define a full analytical description of a RCDPR behaviour to be integrated in the optimal design of spatial continuous RCDPRs?

▪ The design of discrete RCDPR is based on the analysis of a possible set of configurations. The procedure is time consuming and the choice of the set of possible configurations is performed by the designer.

▪ Is it possible to improve the performances of the proposed design strategy?

▪ Is it possible to define a new design strategy that does not rely on the experience of the designer?

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Control


Control #1

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▪ Control schemes are necessary to guide the CDPR and adjust its behaviour.

▪ They integrate several components, including:

▪ The model of the CDPR.

▪ The information provided by the internal and external sensors.

▪ A moving platform trajectory generator.

▪ A control law.

▪ CDPR control scheme and control law are inspired by the developments performed on serial and rigid-link parallel robots, including:

▪ PID control.

▪ Impedance control.

▪ Adaptive control.

➢ S. Fang, D. Franitza, M. Torlo, F. Bekes, and M. Hiller. Motion control of a tendon-based parallel manipulator using optimal tensiondistribution. IEEE/ASME Trans. on Mechatronics, 9(3):561–568, Sept. 2004.

➢ S.-R Oh and S.K. Agrawal. Cable suspended planar robots with redundant cables: Controllers with positive tensions. IEEE Trans. on Robotics,21(3):457–465, June 2005.

➢ C. Reichert, K. Müller, and T. Bruckman. Robust internal force-based impedance control for cable-driven parallel robots. In Cable-DrivenParallel Robots, volume 32 of Mechanisms and Machine Science, 131–143. Springer, 2015.

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Control #2

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▪ Examples of control schemes.

Dual-space adaptive control scheme with joint space controller

➢ S. Fang, D. Franitza, M. Torlo, F. Bekes, and M. Hiller. Motion control of a tendon-based parallel manipulator using optimal tensiondistribution. IEEE/ASME Trans. on Mechatronics, 9(3):561–568, Sept. 2004.

➢ J. Lamaury, M. Gouttefarde, A. Chemori, and P.-E. Herve. Dual-space adaptive control of redundantly actuated cable-driven parallel robots. InProc. of the IEEE Int. Conf. on Robotics and Automation (ICRA 2013), 4879–4886, Tokyo, Japan, Nov. 2013.


Control #3

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▪ Several control schemes have been proposed in the literature.

▪ Which is the best control scheme and the best control architecture, with respect a given task or a given CDPR design?

▪ Control schemes require to compute the model of the CDPR, verify the feasibility of the desired moving platform pose and provide an optimal distribution tension.

▪ How we can integrate all these aspects in the control scheme?

▪ Some research works propose to integrate external sensor in the control scheme.

▪ Which are the most efficient external sensors we can integrate in the CDPR design?

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Conclusions

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▪ CDPR have been widely investigated in the last two decades.


▪ Several advances have been performed in modelling, design and control of CDPRs.

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▪ Lot of working prototypes have been built...

▪ …but several open problems have not be solved, yet !!!

acrobot.MOV

160420_CAROCA_Prototype_Movie1_v2_ordi.wmv

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Communications

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▪ Patents:

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Girin, A. and Yvain, P., 2014, “Robot à câblesreconfigurable et méthode de configuration d’un tel robot”, FR 3024956 (A1), EP 2982483(A2).

▪ Journal articles:

➢ Gagliardini, L., Caro, S., Gouttefarde, and M., Girin, A.„ 2016, “Discrete ReconfigurationPlanning for Cable-Driven Parallel Robots”, Mechanism and Machine Theory, Vol. 100, pp.313 - 337.

➢ “Stiffness Model of Spatial Cable-Driven Parallel Robot with heavy Cables Considering theInfluence of Pulleys”, ongoing

▪ Workshops :➢ Gagliardini, L., Caro, S., Gouttefarde, M., Wenger, P. and Girin, A., “Optimal design of cable-

driven parallel robots for large industrial structures,” Workshop on « Applications of Paralleland Cable-driven Robots », INNOROBO 2014, Lyon, March, 2014.

➢ Gagliardini, L., Caro, S., Gouttefarde, M. and Girin, A., “Optimal Path Planning andReconfiguration for Reconfigurable Cable-Driven Parallel Robots,” Workshop on « OptimalRobot Motion Planning », ICRA 2015, Seattle, Washington, May, 30th, 2015.

Original presentation by Stéphane CARO


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▪ International Conference Articles:

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Wenger, P. and Girin, A., “Optimal Design of Cable-Driven Parallel Robots for Large Industrial Structures”, The 2014 IEEE InternationalConference on Robotics and Automation (ICRA 2014). Hong Kong, China, May 31–June 7,2014.

➢ Gagliardini, L., Caro, S., Gouttefarde, M., Wenger, P. and Girin, A., “A Reconfigurable Cable-Driven Parallel Robot for Sandblasting and Painting of Large Structures”, The SecondInternational Conference on Cable-Driven Parallel Robots (CableCon 2014), Duisburg,Germany, August 24–27, 2014.

➢ Gagliardini, L., Caro, S., Gouttefarde, M. and Girin, A., “A Reconfiguration Strategy forReconfigurable Cable-Driven Parallel Robots”, The 2015 IEEE International Conference onRobotics and Automation (ICRA 2015). Seattle, Washington, May 26th - 30th, 2015.

➢ Gagliardini, L., Caro, S., Gouttefarde, M. and Girin, A., “Dimensioning of Cable-Driven ParallelRobot Actuators, Gearboxes and Winches According to The Velocity Feasible Workspace”,The 2015 IEEE International Conference on Automation Science and Engineering (CASE2015). Gothenburg, Sweden, August 24th - 28th, 2015.

➢ Cruz Ruiz, A. L., Caro, S., Cardou, P. and Guay, F., “ARACHNIS : Analysis of Robots Actuated byCables with Handy and Neat Interface Software”, The Second International Conference onCable-Driven Parallel Robots (CableCon 2014), Duisburg, Germany, August 24–27 2014.

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▪ International Conference Articles:

➢ Cruz Ruiz, A. L., Caro, S., Cardou, P. and Guay, F., 2015, “ARACHNIS : Analysis of RobotsActuated by Cables with Handy and Neat Interface Software”, Cable-Driven Parallel Robots,Mechanisms and Machine Science, Volume 32, pp. 293–305.

➢ Guay, F., Cardou, P., Cruz Ruiz, A. L. and Caro, S., 2014, “Measuring How Well a StructureSupports Varying External Wrenches”, New Advances in Mechanisms, Transmissions andApplications Mechanisms and Machine Science Volume 17, 2014, pp. 385–392.

Design and Modeling of Cable-driven Parallel Robots: State of the Art and Open Issues

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Stéphane CARO

Email: [email protected]

May 26, 2016

design and modeling of cable- driven parallel robots ... · pdf filesince cables cannot push...

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