An Acceleration-based State Observer for Robot Manipulators with Elastic Joints Alessandro De Luca Dipartimento di Informatica e Sistemistica Universit` a di Roma “La Sapienza” Via Eudossiana 18, 00184 Roma, Italy deluca@dis.uniroma1.it Dierk Schr¨ oder Lehrstuhl f¨ ur Elektrische Antriebssysteme Technische Universit¨ at M¨ unchen D-80333 M¨ unchen, Germany Dierk.Schroeder@tum.de Michael Th¨ ummel Institut f¨ ur Robotik and Mechatronik DLR Oberpfaffenhofen D-82234 Wessling, Germany Michael.Thuemmel@dlr.de Abstract— Robots that use cycloidal gears, belts, or long shafts for transmitting motion from the motors to the driven rigid links display visco-elastic phenomena that can be assumed to be concentrated at the joints. For the design of advanced, possibly nonlinear, trajectory tracking control laws that are able to fully counteract the vibrations due to joint elasticity, full state feedback is needed. However, no robot with elastic joints has sensors available for its whole state, i.e., for measuring positions and velocities of both motors and links. Several nonlinear observers have been proposed in the past, assuming different reduced sets of measurements. We introduce here a new observer which uses only motor position sensing, together with accelerometers suitably mounted on the links of the robot arm. Its main advantage is that the error dynamics on the estimated state is independent from the dynamic parameters of the robot links, and can be tuned with standard decentralized linear techniques (locally to each joint). We present an experimental validation of this observer for the three base joints of a KUKA KR15/2 industrial robot and illustrate the control use of the obtained results. I. INTRODUCTION Flexibility of the motion transmission and reduction el- ements in a robot manipulator induce a vibratory behavior that degrades its dynamic accuracy. For industrial robots, this happens when adopting belts or long shafts to drive the links with remotely located actuators, or when harmonic drives or cycloidal gears are used so as to obtain large reduction ratios with compact, in-line, and power efficient devices. Time-varying dynamic displacements will be present on the robot axes, between the position of the motors and that of the driven links. This situation is typically modeled by the introduction of elasticity or visco-elasticity at the joints [1], [2]. The number of independent variables needed to describe the robot dynamics is then doubled with respect to the case of rigid joints. In order to recover performance during fast motion or in quasi-static contact tasks, suitable feedback control laws have to be designed that deal also with joint elasticity, beside facing the nonlinear and highly-coupled dynamics of the robot arm. Dynamic models of different accuracy have been proposed for robots with elastic joints. In the case of electrical actuation, the most common model [3] assumes that the angular kinetic energy of the rotors of the motors is due only to their relative spinning around the driving axes –the so- called reduced model. A more complete dynamic model [4] includes also the inertial couplings existing between the motors and the links. In certain cases, depending on the kinematic architecture of the arm and on the localization of the motors, these couplings may turn to be configuration- independent [5]. These models possess different structural properties from the point of view of control. In particular, the reduced model of robots with elastic joints can be fully decoupled and exactly linearized by means of a nonlinear static state feedback [3], similarly to the well-known com- puted torque method for fully rigid robots. On the other hand, when considering the more complete dynamics, the same result can be achieved only by resorting to a more complex dynamic state feedback [5]. These control results, which are particularly relevant for trajectory tracking tasks, assume the availability of full state measurement of the elastic joint robot, namely of motor as well as link position and velocity. However, a sensory set to directly measure this full state (or an equivalent set of variables) is hardly available. Any robot is equipped with position sensors and these, in the presence of joint elasticity, will typically measure the motor positions. Sometimes, but always more seldom, a tachometer may be present for the motor velocity. Recently, more sensory capabilities have been introduced in prototype arms, e.g., a magnetometer and a joint torque sensor in the DLR lightweight arm [6], [7]. Both allow to measure (directly or indirectly) the link position, but the former is rather noisy while the latter needs the knowledge of the joint stiffness to compute the position from the measured torque. No sensor measuring directly the link velocity is currently in use. This picture motivated the design of state observers to replace missing sensors. There is a variety of existing state observers of elastic joint robots in the literature, assuming different combina- tions of sensed variables: motor position and elastic joint displacement, or link position and motor velocity [8], or link position and velocity and assuming that the latter is bounded by virtue of the control law [9], [10]. Unfortunately, the most successful ones (at least, those with theoretically proved con- vergence) use unrealistic combinations of measured outputs from the robot and typically assume perfect knowledge of the whole robot dynamics. Indeed, the main use of state estimation is for control. Note, however, that regulation tasks can be successfully 2007 IEEE International Conference on Robotics and Automation Roma, Italy, 10-14 April 2007 FrB10.3 1-4244-0602-1/07/$20.00 ©2007 IEEE. 3817