This work describes two use-cases to present strategies for the definition of constrained bimanual manipulation tasks. We use the cooperative dual task-space (CDTS) framework, vector field inequalities (VFIs) and geometric primitives such as Plücker lines and planes to implement collision avoidance with the environment and preserve the integrity of the task. Simulations of the use-cases were carried out and showed that all implemented constraints were upheld through the execution of the bimanual manipulation task

Adorno, Bruno Vilhena

Groves, Keir

Leslie-Dalley, Seyonne

English

The University of Manchester - Institutional Repository

The University of Manchester ResearchControl Strategies for the Task Definition of ConstrainedBimanual ManipulationDocument VersionOther versionLink to publication record in Manchester Research ExplorerCitation for published version (APA):Leslie-Dalley, S., Groves, K., & Adorno, B. V. (2024, Jan 11). Control Strategies for the Task Definition ofConstrained Bimanual Manipulation. Unpublished.Citing this paperPlease note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscriptor Proof version this may differ from the final Published version. If citing, it is advised that you check and use thepublisher's definitive version.General rightsCopyright and moral rights for the publications made accessible in the Research Explorer are retained by theauthors and/or other copyright owners and it is a condition of accessing publications that users recognise andabide by the legal requirements associated with these rights.Takedown policyIf you believe that this document breaches copyright please refer to the University of Manchester’s TakedownProcedures [http://man.ac.uk/04Y6Bo] or contact uml.scholarlycommunications@manchester.ac.uk providingrelevant details, so we can investigate your claim.Download date:24. May. 20241Control Strategies for the Task Definition ofConstrained Bimanual ManipulationSeyonne Leslie-Dalley, Keir Groves, Bruno Vilhena AdornoAbstract—This work describes two use-cases to present strate-gies for the definition of constrained bimanual manipulationtasks. We use the cooperative dual task-space (CDTS) framework,vector field inequalities (VFIs) and geometric primitives suchas Plücker lines and planes to implement collision avoidancewith the environment and preserve the integrity of the task.Simulations of the use-cases were carried out and showed thatall implemented constraints were upheld through the executionof the bimanual manipulation task.I. INTRODUCTIONCooperative control of two or more manipulators allows forthe completion of a broader range of tasks that would have oth-erwise been infeasible for a single manipulator [1]. Althougha suitable control strategy is required to fulfill the cooperativetask, it is also essential that a collision avoidance techniqueis implemented to ensure the safety of the manipulators andpreserve the manipulated object [2].Marinho et al. [3] developed a novel method for implemen-tation of explicit constraints directly in closed-loop controllaws using Vector Field Inequalities (VFIs), preventing robotsfrom entering restricted regions or alternatively being enclosedin a safe region. Their framework used dual quaternionalgebra due to the advantages it has over other represen-tations, such as being compact, free from representationalsingularities, and able to represent several geometric primitivesstraightforwardly [4]. Quiroz-Omaña and Adorno [5] coupledthe methods in [3] with the Cooperative Dual Task Space(CDTS) framework proposed in [6] to prevent the violationof joint limits and undesired end-effector orientations whilstcompleting bimanual manipulation tasks on a two-arm mobilemanipulator.Similar to [5], we also use the CDTS framework and VFIs.However, instead this work presents two use-cases of parallelcoordinated bimanual manipulation tasks [7]. The use-casespresent how these methods can be applied to two fixed-base manipulators so that they can complete a cooperativemanipulation task while explicitly accounting for constraintsrelated to obstacles as well as end-effector poses.II. CONTROL STRATEGYThe closed-loop kinematic controller implements a linearly-constrained quadratic optimization problem where hard con-staints such as obstacle avoidance and joint limits are enforcedAll authors are with the Manchester Centre of Robotics andAI at the University of Manchester. E-mails: seyonne.leslie-dalley@postgrad.manchester.ac.uk, keir.groves@.manchester.ac.uk, andbruno.adorno@.manchester.ac.uk.This project was funded by EPSRC through the CRADLE programme(EP/X02489X/1).as differential inequalities in the control input. Considering adesired task variable xd ∈ Rm and the task error x̃ , x − xd,the control input u is obtained fromu ∈ argminq̇‖Jq̇ + ηx̃‖22 + λ2 ‖q̇‖22subject to W qq̇  wq,(1)where J ∈ Rm × n is the relevant task Jacobian, η ∈ (0,∞)is the proportional gain that determines the convergencerate, and λ ∈ (0,∞) is the damping factor used to pe-nalise high joint velocities. In addition, the matrix W ,W ∈ Rp × n and the vector w , w∈Rp impose p linearconstraints on the control input necessary to complete the task.III. MANIPULATION TASKSThe following section describes two bimanual manipulationtasks. Each task defined uses primitives from the CDTSframework [6] for task relaxation, thus releasing degrees offreedom (DOFs) to enforce constraints. The constraints aredefined using VFIs and geometric primitives such as planesand cones determined by Plücker lines.A. Carrying and Balancing ObjectsThe goal is to move an object whilst maintaining a certainorientation, which is useful when moving a tray with a cupwhile minimising spillages. The desired movement can bedefined in respect to a translation of the held object witha bounded orientation, whilst the relative pose of the end-effectors is kept constant to hold the object. This task can besplit into two main sub-tasks:1) Maintaining contact with the object.2) Maintaining the cup orientation below a threshold toprevent spillage.Firstly, to ensure the relative pose xr is constantly kept withina threshold, the following inequality is defined,2 (xr − xrd) TJrq̇ ≤ −η(‖xr − xrd‖22 − dmax),where xr and xrd denote the current relative pose and thedesired relative pose, Jr denotes the Jacobian of the relativepose and dmax is the maximum allowed deviation from thedesired relative pose. This is then implemented as an inequalityconstraint in the controller (1). Secondly, the cup orientation isconstrained by defining two Plücker lines—one always verticalpassing through the center of the held object and the otherdynamic—and constraining the angle between them by usinga conic constraint [8], as shown in Fig. 1a.2B. Carrying and Transporting Large/Heavy ObjectsTo transport an object to a desired region while avoidingcollisions with the environment, the task variable can bedefined similar to III-A. Alternatively, it can be defined byminimising the distance between the object and a definedregion. Similar to III-A, a relative pose error inequality is alsodefined to maintain contact with the object.Assuming walls and the floor are modelled using planes,then VFIs can be used for collision avoidance by describingthe distance functions between planes and the collidableentities (e.g., cylinders, spheres, cuboids) associated with thetransported object and their corresponding distance Jacobians[3].IV. SIMULATIONS AND DISCUSSIONSWe performed simulations of manipulation tasks describedin Sections III-A and III-B. The tasks were simulated usingCoppeliaSim1 for visualisation and DQ Robotics [9] to modeland control the manipulators and define the geometric primi-tives used in the constraints. The setup for the simulations areshown in Fig. 1, where two UR5 manipulators with six DOFswere used to complete the bimanual manipulation tasks. Forthe task of balancing an object, the maximum angle the tray isallowed to tilt is φmax = 0.05 rad, and the maximum deviationfrom the relative pose is dmax = 0.03 to prevent deformingthe tray. For the task of moving an object shown in Fig. 1b,the safe distance from the walls represented by red planes aregiven by dwall = 0.05m and the maximum deviation from therelative pose is given by dmax = 0.03.Fig. 2 shows that the conic constraint and the relative poseerror constraint were respected during the execution of thecarrying-and-balancing an object task. Additionally, Fig. 3shows that for the transportation task both the relative distanceand the plane constraints were upheld, as expected.(a) Balancing an object. (b) Transportation of an object.Fig. 1. In (a), the angle between the black vertical Plücker line and the onecollinear with the green arrow must be smaller than the half-angle of the redcone to prevent spillage. In (b), the green sphere defines the desired regionfor the centre of the object, and the red planes define walls and the floor inthe environment.V. CONCLUSIONThis work described two use-cases to present strategies fordefining bimanual manipulation tasks using VFIs. Simulations1https://www.coppeliarobotics.com/coppeliaSim0 100 200Iteration00.020.040.06?lz ;l(rad)0 100 200Iteration00.010.020.03kxr ! xrdk0 100 200Iteration00.20.40.6k~xkFig. 2. From left to right: the tilting angle with respect to a vertical line;norm of the relative pose error; norm of the task error. Dashed lines representthe constraints.0 500Iteration00.511.5dpi;n:i0 500Iteration00.010.020.03kxr ! xrdk0 500Iteration00.20.40.6k~xkFig. 3. From left to right: the distance from either end of the object to thetwo walls and the floor; norm of the relative pose error; norm of the taskerror. Dashed lines represent the constraints.of the use-cases have shown that constraints are enforcedthroughout the task execution. Future works will focus ondeveloping the CDTS framework to include the extension pro-posed by [7] to represent both coordinated and uncoordinatedbimanual manipulation tasks and further implement constraintswithin the extended framework.REFERENCES[1] F. Caccavale, P. Chiacchio, and S. Chiaverini, “Task-space regulation ofcooperative manipulators,” Automatica, vol. 36, pp. 879–887, 2000.[2] M. Moletta and M. Tadiello, “Comparison of collision avoidance al-gorithms for autonomous multi-agent systems,” Proceedings - 2020IEEE 44th Annual Computers, Software, and Applications Conference,COMPSAC 2020, pp. 1–9, 7 2020.[3] M. M. Marinho, B. V. Adorno, K. Harada, and M. Mitsuishi, “Dynamicactive constraints for surgical robots using vector-field inequalities,” IEEETransactions on Robotics, vol. 35, pp. 1166–1185, 10 2019.[4] B. V. Adorno, “Robot kinematic modeling and control based on dualquaternion algebra-part i: Fundamentals,” 2017. [Online]. Available:www.ppgee.ufmg.br/~adorno[5] J. J. Quiroz-Omana and B. V. Adorno, “Bimanual mobile manipulationusing the cooperative dual task-space framework and vector fieldsinequalities,” Workshop on Applications of Dual Quaternion Algebrato Robotics, pp. 1–2, 12 2019. [Online]. Available: https://zenodo.org/record/3566806[6] B. V. Adorno, P. Fraisse, and S. Druon, “Dual position control strate-gies using the cooperative dual task-space framework,” IEEE/RSJ 2010International Conference on Intelligent Robots and Systems, IROS 2010- Conference Proceedings, pp. 3955–3960, 2010.[7] H. A. Park and C. S. Lee, “Extended cooperative task space for ma-nipulation tasks of humanoid robots,” Proceedings - IEEE InternationalConference on Robotics and Automation, vol. 2015-June, pp. 6088–6093,6 2015.[8] J. J. Quiroz-Omana and B. V. Adorno, “Whole-body control with (self)collision avoidance using vector field inequalities,” 6 2019. [Online].Available: http://arxiv.org/abs/1906.07322http://dx.doi.org/10.1109/LRA.2019.2928783[9] B. V. Adorno and M. M. Marinho, “DQ Robotics: A libraryfor robot modeling and control,” IEEE Robotics & AutomationMagazine, vol. 28, no. 3, pp. 102–116, Sep. 2021. [Online]. Available:https://ieeexplore.ieee.org/document/9136790/

Control Strategies for the Task Definition of Constrained Bimanual Manipulation

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Control Strategies for the Task Definition of Constrained Bimanual Manipulation

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