Two-loop decentralized admittance control for a multi-manipulator system

Two-loop decentralized admittance control for a multi–manipulator system Graziano Carriero, Monica Sileo, Francesco Pierri Department of Engineering University of Basilicata Potenza, Italy Sebastiano Fregnan⋆, Marko Guberina⋆, Yiannis Karayiannidis⋆ Department of Automatic Control Lund University Lund, Sweden Fabrizio Caccavale Department of Health Sciences University of Basilicata Potenza, Italy Abstract—The proposed decentralized strategy for cooperative object transportation consists of two steps. First, each robot estimates the wrenches applied to the object by all the other robots. Second, an admittance control scheme is used to limit internal wrenches.Experiments have been carried out with ABB Dual-arm YuMi and a UR5e robot, confirming the effectively reduction of internal wrenches. Index Terms—Decentralized control, cooperative manipulation, multi-manipulator system I. INTRODUCTION Collaborative robot teams have been recently employed to reduce physical demands on human operators in tasks beyond the capabilities of a single agent, such as transporting large or heavy objects [1]. Moreover, decentralized and distributed strategies for cooperative control have been currently developed to improve scalability and robustness. In multi-robot systems, particularly for transportation tasks, managing the wrenches exchanged with manipulators and the environment is a critical challenge. These wrenches must be controlled to minimize internal stresses that could compromise object integrity. Impedance and admittance control schemes [2], [3] are effective in regulating the interaction between the object and the environment. II. OBJECT DYNAMICS In the absence of interaction with the external environment, the object dynamics, can be written as Mo(xo)¨ xo+Co(xo,˙ xo)˙ xo+go=I3O3 O3T(ϕo)T ho, where xo= [pT oϕT o]T(˙ xo,¨ xo) is the object pose (generalized velocity, generalized acceleration), containing the object position and orientation, Mois the inertia matrix, Cois the matrix of the centripetal and Coriolis terms, gois the gravity term, hois the vector of wrenches exerted by the manipulators on the object and T(ϕo)is the matrix relating the derivative of the Euler angles, ˙ ϕo, to the object angular velocity, ωo. The wrench exerted on the object by the manipulators’ endeffectors is ho=G he,(1) ⋆Member of the ELLIIT Strategic Research Area at Lund University. This research was funded by the Next Generation EU-Italian National Recovery and Resilience Plan (NRRP), Mission 4, Component 1, under the program PRIN 2022 PNRR of the Italian Ministry of University and Research. Project MELODY (Multi robot collaborativE manipuLation suppOrting DisassemblY tasks) CUP C53D23008320001. where Gis the grasp matrix [4] and hecollects the wrenches exerted by each manipulator at its grasping points, i.e., he= hhT 1hT 2. . . hT NiT . Since Ghas full row rank, an inverse solution of (1), proposed by [5], is he=G†ho+V hi=hE+hI,(2) where G†is a right pseudo-inverse of G,V∈IR6N×(6N−6) is a full column rank matrix spanning the null space of G, and hi∈IR6N−6collects the independent wrenches that does not contribute to the object motion, usually referred as internal wrenches. The wrench balancing the object’s dynamics, hE, is given by hE=hhT E1hT E2. . . hT ENiT=G†Ghe,(3) while hI, i.e., the collection of the robot contributes to the internal wrench, is hI=hhT I1hT I2. . . hT INiT=V hi=V V †he.(4) III. DECENTRALIZED WRENCH ESTIMATION The internal wrench on the object remains unknown to the manipulators, since, in view of (4), it depends on the wrenches exerted by all the teammates. To overcome this drawback, in order to estimate all the wrenches exerted on the object, each manipulator runs a bank of N−1consensus-based estimators. Thus, the estimate of the wrench exerted by the k-th manipulator (k= 1, . . . , N) on the object computed by the i-th manipulator, iˆ hk, is obtained by i˙ ˆ hk(t)=k0X j∈Nijˆ hk(t)−iˆ hk(t),(5) where k0is a positive scalar gain. Based on the previous equation, each robot can estimate its own contribute to the internal wrenches defined in (4) as ˆ hIi=ΓiV V †iˆ he,(6) where Γi={O6· · · I6 |{z} i-th robot · · · O6}∈IR6×6N. IV. DECENTRALIZED ADMITTANCE CONTROL The local admittance controller receives as input the desired trajectory of the i-th end-effector and the estimate ˆ hIiof the i-th robot contribute to the internal wrenches (6). The output is a reference trajectory, in terms of end-effector pose and generalized velocity and acceleration, computed as 2025 I-RIM Conference October 17-19, Rome, Italy ISBN: 9788894580570 10.5281/zenodo.17629652 69 Robot 1Robot 0 Robot 2 Fig. 1. The communication graph among the 3robots. ¨ xri=¨ xdi+M−1 iKDi(˙ xdi−˙ xri) + +KPi(xdi−xri)+ΓiV V †iˆ he,(7) where KDi,KPiand Miare (6×6) positive definite matrices of gains, representing, respectively, a virtual damping, stiffness and inertia imposed to the i-th end-effector motion. Assumption 1: The connection between the i-th end-effector is modeled by introducing a grasp reference frame attached to the object linked to the i-th end-effector frame by a 6-DOFs spring system. V. EXPERIMENTAL RESULTS Consider a cooperative robotic cell composed of N= 3 arms (Fig. 1), a UR5e manipulator from Universal Robots and a dual-arm ABB YuMi robot, in charge of transporting a square-shaped wooden piece, whose size is 30 ×30 ×0.5 cm, with mo= 0.250 kg mass, in a decentralized manner. At each time instant, the i-th robot receives the sensed wrench from its force-torque sensor, hi, and the wrenches estimation of its neighbours, iˆ hj=i. Then, via (5), the i-th robot estimates the end-effector wrench collective vector iˆ he. Finally, by exploiting (7), each robot computes the reference trajectory in terms of position, velocity and acceleration. The desired object barycenter trajectory consists of a translation along an arc of circumference with radius r= 0.15 m and angle θp=π/6rad, and a rotation along the z-axis of an angle θo=π/6rad. A comparison with a pure positional controller has been carried out in order to test the effectiveness of the proposed estimator-controller architecture. Figure 2 compares the internal force and torque contributions of Robot 2 on the object, hI2, in both the experiments. The internal wrenches reduction experienced with the proposed approach is remarkable, as well as the boundedness of the internal forces and torques. In the absence of the admittance control both fIx,2and τIz,2increase to dangerous levels. Conversely, this substantial decrease in internal wrenches does not result in any significant alteration in the trajectory commanded to the object, whose tracking errors are not affected by the presence of admittance controller, as depicted in Fig. 3. Errors are comparable with both approaches and can be mainly attributable to the wrench model adopted in Assumption 1. Finally, low-level control tracking errors are not reported since they are negligible. REFERENCES [1] X. An, C. 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