A Dynamical System Approach to Motion and Force Generation in Contact Tasks

Abstract

Many tasks require the robot to enter in contact with surfaces, be it to take support, to polish or to grasp an object. It is crucial that the robot controls forces both upon making contact and while in contact. While many solutions exist to control for contact, none offer the required robustness to adapt to real-world uncertainties, such as sudden displacement of the object prior and once in contact. To adapt to such disturbances require to re-plan on the fly both the trajectory and the force. Dynamical systems (DS) offer a framework for instant re-planning of trajectories. They are however limited to control of motions. We extend this framework here to enable generating contact forces and trajectories through DS. The framework allows also to modulate the impedance so as to show rigidity to maintain contact, and compliance to ensure safe interaction with humans. We validate the approach in single and dual arm setting using KUKA LWR 4+ robotic arms. We show that the approach allows 1) to make smooth contact while applying large forces, 2) to maintain desired contact force when scanning non-linear surfaces, even when the surface is moved, and 3) to grasp and lift smoothly an object in the air, and to re-balance forces on the fly to maintain the grasp even when subjected to strong external disturbances.

Force Adaptation in Contact Tasks with Dynamical Systems

“…In this work, the DS is applied only to the translation of the endeffector. To control the desired end-effector's orientation we use the axis-angle representation (see [23] for more details). In short, from the measured and desired orientation, the taskspace torque is computed using a PD-like control law.…”

“…The first term represents the driving force along the nominal dynamics, the third term is the damping force, while the second term denotes the modulation force along the normal direction to the surface that we design in [23] as:…”

“…A sufficient condition to achieve stability is to ensure passivity of the whole system [28], [29]. In [23], we achieve passivity through the use of energy tanks [30]. The formulation described in [23] still holds for this work.…”

“…These works could however only control for stiffness at contact but not for the amount of force applied. Recently, in [23], we extended this framework to control explicitly for the amount of forces when coming in contact with the object. The strategy is based on local modulation of the robot's nominal motion to generate contact forces when the robot is close to the target surface.…”

“…The robot can learn and adapt online to these errors through the interaction with the surface. In this work, we extend the approach presented in [23] to deal with uncertainties and improve the force tracking performance through on-line learning of a state-dependent force correction model. The advantage of learning a state-dependent force compensation is that the online adaptation can be deactivated once the error has been sufficiently reduced and the learned profile can be re-used later without the need to re-learn.…”