A spatial impedance controller for robotic manipulation

Abstract

Abstract-Mechanical impedance is the dynamic generalization of stiffness, and determines interactive behavior by definition. Although the argument for explicitly controlling impedance is strong, impedance control has had only a modest impact on robotic manipulator control practice. This is due in part to the fact that it is difficult to select suitable impedances given tasks. A spatial impedance controller is presented that simplifies impedance selection. Impedance is characterized using "spatially affine" families of compliance and damping, which are characterized by nonspatial and spatial parameters. Nonspatial parameters are selected independently of configuration of the object with which the robot must interact. Spatial parameters depend on object configurations, but transform in an intuitive, well-defined way. Control laws corresponding to these compliance and damping families are derived assuming a commonly used robot model. While the compliance control law was implemented in simulation and on a real robot, this paper emphasizes the underlying theory.

Admittance Selection for Force-Guided Assembly of Polygonal Parts Despite Friction

“…If we denote then the total contact wrench is (4) By the control law (1), the motion of the rigid body is given by (5) To maintain contact [13], the reciprocal condition requires Substituting (5) into this and solving for , we have (6) Substituting this result back into (5) yields the following equation for constrained motion:…”

“…Asada [4] used a similar optimization procedure for the design of an accommodation neural Manuscript network rather than an accommodation matrix. More recently, Fasse and Broenink [5] and Marcelo et al [6] provided synthesis procedures based on spatial intuitive reasoning. None of these approaches, however, ensures that the admittance selected will, in fact, be reliable for a specified range of friction coefficients and part misalignments.…”

Impedance Behaviors for Two-handed Manipulation: Design and Experiments

“…Caccavale and Natale investigated the rotational part of the stiffness based on different orientation representations [9], [10]. Spatial stiffness controllers including a coupling stiffness term between translation and rotation were proposed in the works of Fasse and Zhang [11]- [13]. Stramigioli analyzed the power flow for these springs when the rest length 1 and the stiffness values are subject to changes [14].…”

“…One simple, but effective, possibility to implement an impedance behavior for joint limit avoidance is to use another potential function V l (θ) in superposition with (10), (12) or (11). Let θ i denote the i th element of θ and θ i,min and θ i,max its minimum and maximum value.…”

A rigorous framework for interactive robot control

“…This section presents a non-trivial example to illustrate the utility of the framework for analysing spatially complex interaction controllers.`Spatial compliance control' (Fasse and Broenink 1997) is a Euclidean-geometric method for controlling the mechanical compliance of a robotic end-e ector. Unlike well-known compliance control methods this method does not use generalized coordinates, so it cannot be analysed using conventional methods.…”