A supervisory loop approach to fulfill workspace constraints in redundant robots

Abstract

ElsevierGracia Calandin, LI.; Sala, A.; Garelli, F. (2012). A supervisory loop approach to fulfill workspace constraints in redundant robots. Robotics and Autonomous Systems. 60 (1) AbstractAn approach based on geometric invariance and sliding mode ideas is proposed for redundancy resolution in robotic systems to fulfill configuration and workspace constraints caused by robot mechanical limits, collision avoidance, industrial security, etc. Some interesting features of the proposal are that: (1) it can be interpreted as a limit case of the classical potential fieldbased approach for collision avoidance which requires using variable structure control concepts, (2) it allows reaching the limit surface of the constraints smoothly, depending on a free design parameter, and (3) it can be easily added as a supervisory block to pre-existing redundancy resolution schemes. The algorithm is evaluated in simulation on a 6R planar robot and on the freely accessible 6R robot model PUMA-560, for which the main features of the method are illustrated.

Robot coordination using task-priority and sliding-mode techniques

“…It will allow a simple computer implementation, in the line of other proposals by the authors [13,14], fulfilling the constraints specified by the robot end-user without recourse to high-level planning.…”

“…However, if minor deviations can be allowed (for instance, in lower-level tasks), this drawback can be overcome using matrix regularization for A i N i−1 in the computation ofq c,i in (13). A classical type of regularization is the damped least-squares (DLS) solution [29] that consists of minimizing the square norm of the equation error together with the square norm of the solution weighted by a nonnegative damping factor λ.…”

“…Such theory has been successfully adapted by the authors to tackle some particular problems in single-robot configurations [12,13] and is also at the heart of the proposals in this work.…”

“…In particular, one set of sufficient, but not necessary, conditions for making the set Φ invariant are that matrix L g φ is full row rank and that [13]:…”

“…In order to fulfill equality and inequality constraints, or reaching such feasible regions in finite time if not initially in them, sliding-mode (SM) control theory has been used in literature [9,10], in particular geometric-invariance approaches [11]. Previous work by the authors discusses how sliding-mode geometric invariance can be used to solve some problems in single-robot systems [12,13,14], while the third author has preliminarily evaluated its effectiveness for the coordination of single scalar realizable references commanding input-constrained dynamical systems [15,16]. The objective of this work is generalizing the above ideas to deal with MRSs as well as incorporating constraint prioritization situations.…”