Proceedings of zyxwvutsrqpo the 1999 IEEYASME International Conference on Advanced Intelligent Mechatronics September 19-23.1999 Atlanta, USA zyxwvutsrqp Robust Hybrid Force/Position Control with Experiments on an Industrial Robot Ciro Natale, Bruno Siciliano, and Luigi Villani PRISMA Lab, Dipartimento di Informatica e Sistemistica Universita degli Studi di Napoli Federico I1 Via Claudio 21, 80125 Napoli, Italy zyxwv E-mail: {natale,siciliano ,villani}@disna. dis .mina.it URL: http://disna.dis.unina.it/prisma Abstract-The aim of this paper is to report the results of an experimental investigation of hybrid force/position con- trol algorithms for a robot manipulator, whose end effec- tor is in contact with a nearly rigid spherical surface. The model of the constrained robot is derived using the clas- sical Lagrangian multiplier approach. An inverse dynam- ics strategy is adopted to design the hybrid force/position controllers, comprising a proportional-derivative (PD) ac- tion on position, and either a proportional (P) action or a proportional-integral (PI) action on force. Then, in or- der to robustify the system in practical implementation, a parallel force/position control strategy is adopted along the constrained direction. Two typical contact tasks are exe- cuted and the various control algorithms are tested on an industrial robot with open control architecture and 8 wrist force sensor. I. INTRODUCTION When a robot manipulator is required to interact with a rigid environment, its end effector shall maintain contact with the surface profile while ensuring suitable values of the contact force. For this reason, the environment is typically modeled in terms of an algebraic equation to be satisfied by the end-effector position coordinates, which in turn sets a constraint for the robot dynamic model. By using the classical Lagrangian multiplier approach [l], the resulting model is cast in a form where the constrained and unconstrained task variables are clearly separated. This naturally leads to the hybrid force/position control paradigm [2], according to which the contact force shall be controlled along the constrained directions whereas the end-effector position shall be controlled along the uncon- strained directions. In order to guarantee tracking of the end-effector position and tracking (or at least regulation) of the contact force, an inverse dynamics strategy can be pursued in the hybrid framework where the constfaints can be expressed either in the task space [3], [4] or i n the joint space zyxwvutsrq [5]. The aim of this work is to investigate the performance of various hybrid force/position controllers with inverse dy- namics and task space constraints in a number of experi- mental tests on a commercially available industrial robot. The robot in the lab is endowed with an open control ar- chitecture and a wrist force sensor. Its end effector is in contact with a nearly rigid spherical surface. Initially, a PD action is designed for the position control loop, whereas a P action is designed for the force control loop. Then, in order to avoid instabilities at the contact, the P action is replaced with a PI action. Finally, a robustifying action is devised where a parallel force/position control strategy is adopted along the constrained direction, which consists of introducing a PD action on position in parallel to the PI ac- tion on force. The results for two typical contact tasks are illustrated and critically compared throughout the paper. 11. MODELING OF CONSTRAINED ROBOT For the purpose of the present work, a three-degree-of- freedom robot manipulator is considered, whose end effec- tor is in contact with a rigid and frictionless environment. The contact surface is a sphere of radius zyxw R. By adopting a set of spherical coordinates x= [i] with reference to a frame with origin in the center of the sphere, the constraint can be simply described by zyx p=R. In view of this choice, the contact force is aligned with the radial direction and thus it is given by (3) On the other hand, it is convenient to express the robot dynamic model in the task space [6], where the end-effector position is described by the spherical coordinates in (l), i.e. B(z)% zyxw + n(2, *) = U - zy f (4) where B is the (3 x 3) symmetric positive definite inertia matrix, n is the (3 x 1) vector of Coriolis, centrifugal and gravity forces, and U is the (3 x 1) vector of equivalent end- effector driving forces. The (3 x 1) vector 7 of joint driving torques can be computed as [7] 7 = JT(q)u, (5) 0-7803-5038-3/99/$10.00 0 1999 IEEE 956