Soft robotics: what Cartesian stiffness can obtain with passively compliant, uncoupled joints?

Abstract

In the field of service robotics, whole arm contact with an U I W~N C~U E~ environment or human beings becomes a major issue. Therefore son robots, which means robots with passively (or mechanically) compliant joints, hecame more and mom important. In this work we analyze what Cartesian stiffness at the tool center point one can achieve with a passively compliant, redundant robot with variable joint stiffness. We restrict this work to the special case of uncoupled joint stiffness only, as coupling of joint stiffness Seems to be mechanically difficult to realize. Finally we discuss a Cartesian controller which incorporates the compliance of the joints and ensures the correct stifTmss behavior also for high displacements from the desired position.

Configuration-based compliance control of kinematically redundant robot arm Part I: Theoretical framework

“…Generalized stiffness matrix (2) is physically nonhomogeneous. Therefore, it can be interpreted as a block matrix composed of four physically homogeneous blocks (submatrices): K Ttranslational stiffness block, K R -rotational stiffness block, and K TR and K RT -coupling blocks which represent interrelation (crosstalk) between the translational and rotational displacements of the robot TCP, [13]. Diagonal blocks K T and K R are full submatrices, which implies that coupling phenomenon is also present within the physically homogeneous subdomains.…”

“…As stated in [13], the second term in (7b) can be neglected since the joint displacement vector δq is very small when the robot arm TCP is close to its equilibrium configuration (δq ≈ 0). This leads to the simplified relation which is well known from the early stages of research in the field of active stiffness control, [3]:…”

“…According to the relation (13), an arbitrary joint displacement vector δq 0 should be determined in a way to satisfy a suitable cost function u(q), which is related to the objectives specified within the Proposition #1. The cost function u(q) is an appropriate measure of the loss of performances, or the discrepancy between the desired robot TCP stiffness K xd and induced robot TCP stiffness K x which is governed by its current configuration q and the stiffness of its joints k q_ii (the diagonal elements of the jointspace stiffness matrix).…”

“…In other words, rather than dealing with the control, efforts have been predominantly focused on stiffness modelling, identification and characterization. Probably the most relevant research results are presented in [13] where three cost functions are proposed for the general framework for robot TCP stiffness control, defined as an optimization problem which is based on minimization of the following functional:…”

“…The concept of Conservative Congruence Transformation (CCT) allows implementation of a joint level stiffness matrix without the off-diagonal elements. Theoretical analysis and an optimization solution for the problem of inducing a desired taskspace stiffness based on the CCT concept and kinematically uncoupled joints are given in [13].…”