Control for cooperative robot systems in tasks of manipulation in interaction with the environment

A control scheme for a cooperative system consisting of ABB robotics arms is developed to perform manipulation tasks. The mathematical model of the object and the contact points is obtained by, analyzing internal and external forces/torques generated by the cooperative system according to geometry and stiffness of the object surface. A hybrid position/force-torque control system is implemented, which is formed by an internal PID position control loop and an external PI force-torque control loop, this scheme guarantees grip in the object handling. The cooperative system is reactive, this allows us to generate both, translation and rotation movements by a differential of force and torque respectively, a hybrid extended position/force-torque control is implemented to yield a differential. 1.INTRODUCTION A manipulator robot is a mechanism formed generally by elements in series, articulated with each other, intended for the subjection or displacement of objects. Despite the wide range of activities that a manipulator robot can perform on its own, there are tasks for which the manipulation ability or versatility are limited, such as the manipulation of large objects whose weight can exceed the robot working capacity, to perform these tasks a system of cooperative manipulative robots is necessary. The cooperative robotic systems demand in the industry is increasing due to the complexity of tasks that are currently being developed. When performing manipulation or grabbing, the cooperative system is in constant interaction with the object and the environment, according to the object/environment physical properties there are tasks where the implementation of a position control is not enough. Therefore, the force/torque control is important to know the force/torque generated by the cooperative system which could cause deformations to the object/environment, the hybrid position/force-torque control scheme encompasses 1) Student 2) Professor 3) Professor The 2019 World Congress on Advances in Nano, Bio, Robotics and Energy (ANBRE19) Jeju Island, Korea, September 17 21, 2019 position and force/torque control. The force/torque control is based on a capacitive impedance model, in which forces and torques of reaction are generated by the penetration that exists on the object surface (Caccavale 2008). An important point to perform the manipulation and grasping tasks is the study of internal and external forces/torques, that are generated by the cooperative system interacting with the object (Carbone 2013). In manipulation tasks, two phases are proposed, first the grasping phase, in which the final effectors have contact with the object surface, the position/force-torque hybrid control is implemented to perform a grasping applying a desired force, in the second phase, which is the planning of rotational and translational movement maintaining the grasp, a hybrid extended position/force-torque control is implemented. The control scheme experimental implementation is carried out on a cooperative system consisting of two ABB robots equipped with force sensors of 6 degrees of freedom at the final effector. 2. MODELING The cooperative system consists of two robotic arms of six DOF, the dynamic model of each robotic arm is presented with free dynamics when the end effector does not interact with a reaction force that opposes its movement, and a constrained dynamics when there is interaction with the object/environment, generating reaction forces at the end effector. When performing manipulation or grasping tasks there is an interaction between the two robots that make up the cooperative system and the object to be manipulated, so the robotic arms present a constrained dynamics (Siciliano 2009), which for each robot arm ( i=1,2) is given by Eq. (1), Di qi qi + Ci qi , qi qi + Qiqi + gi qi = τi + Ji 𝑕i (1) where Di qi is the positive definite symmetric inertia matrix, Ci qi , q i is the centrifugal and Coriolis forces matrix, Qi is the viscous friction coefficients matrix, gi qi is the gravitational forces vector, qi is the vector of generalized joint coordinates, τi is the input torque vector, Ji is the Jacobian matrix, 𝑕i is the forces and moments acting at the end effector vector. The cooperative system dynamic model is compactly written as shown in Eq. (2), D q q + C q, q + Qq + g q = τ + J𝑕 (2) where D q = blockdiag D1 , D2 , C q, q = blockdiag C1 , C2 , g q = g1 T , g2 T T Q = blockdiag Q1 , Q2 , J = blockdiag J1 , J2 , τ = τ1 T , τ2 T , 𝑕 = 𝑕1 T , 𝑕2 T , q = q1 T , q2 T . When the robotic arms interact with the object, their movement is dynamically coupled, for this reason it is important to know the object dynamics. Consider the The 2019 World Congress on Advances in Nano, Bio, Robotics and Energy (ANBRE19) Jeju Island, Korea, September 17 21, 2019 known object surface S x, y, z = 0, and the center of mass of the object as the reference frame Σe , as show in Fig. 1. Fig. 1 Grip of an object, a) Resultant force, b) Resultant torque The generalized forces applied at the contact points 𝑕1, 𝑕2 are directed to the center of mass, producing two resultant forces, the external force he generates translational movement at the object, and the internal force hi, which generates mechanical stresses in the object. If the generalized forces are not directed to the center of mass, Fig. 1b, they yield two resultant torques, an external torque that generates a rotational movement of the object, where the rotation pivot is the center of mass of the object, and an internal torque generating mechanical stresses. When performing manipulation or grasping tasks, each end effector exerts a force Fi and a torque Mi at the contact points of the object which are call generalized forces 𝑕i . The grasping matrix W = w1, w2 , maps these forces to the object reference system Σe . Eq. (3) 𝑕e = w1 , w2 𝑕1 T , 𝑕2 T T = W𝑕 (3) where, wi = I3 O3 −S ri I3 (4) S . is an antisymmetric matrix operator, ri is called virtual tensor. The dynamic equation of the object can be expressed as, Eq. (5) Meve e + Ce ve e ve e + ge e = 𝑕e e (5) where, Me = meI O O Je e , Ce ve e = meS ωe e O O S ωe e Je e , The 2019 World Congress on Advances in Nano, Bio, Robotics and Energy (ANBRE19) Jeju Island, Korea, September 17 21, 2019 ge e = −meg0 e 0 , ve e = pe e ωe e ,