On the Spatial Compliance of Robotic Manipulators

Abstract

Interactive control schemes, such as stiffness control and impedance control, are widely accepted as a means to actively accommodate environmental forces, but have not been widely applied. This is in part because well-known controllers are parametrized in a mathematically convenient, but nonintuitive way. “Spatial compliance control” is a Euclidean-geometrical version of compliance control that is parametrized in an intuitive way. A family of compliances is introduced with spatial transformation properties that simplify spatial reasoning aspects of compliance parameter selection. A control law is derived assuming that the robot consists of a serial linkage of rigid links actuated by variable-effort actuators.

Comparison of object-level grasp controllers for dynamic dexterous manipulation

“…In this appendix we provide one example implementation of a potential function related to a spatial spring between the frames H 1 = [R 1 , p 1 ] and H 2 = [R 2 , p 2 ]. Similar implementations with slightly different properties can be found in Fasse (1997), Caccavale (et al), Zhang and Fasse (2000), and Stramigioli and Duindam (2001). The potential function is split into a translational and a rotational part…”

“…Similar implementations with slightly different properties can be found in Fasse (1997), Caccavale (et al), Zhang and Fasse (2000), and Stramigioli and Duindam (2001). The potential function is split into a translational and a rotational part V s ( H 1 , H 2 , K) = V t ( p 1 , p 2 , K) +V r ( R 1 , R 2 , K) .…”

Impedance Behaviors for Two-handed Manipulation: Design and Experiments

“…One simple way how to use V l (θ) for joint limit avoidance is to superimpose it with (12). In case that the joint limit avoidance should effect only the redundant nullspace motion, then instead of (2) one should use a controller of the form…”

“…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.…”

“…10). We commanded translational motion on object-level using the control law (14) and the potential function (12) applied to the complete upper body system. Accordingly, all joints of Justin contributed to the object motion.…”