Partially Flagged Parallel Manipulators: Singularity Charting and Avoidance

• Published in: IEEE transactions on robotics Vol. 25; no. 4; pp. 771 - 784
• Main Authors: Alberich-Carraminana, M., Garolera, M., Thomas, F., Torras, C.
• Format: Journal Article Publication
• Language: English
• Published: New York, NY IEEE 01-08-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Applied sciences; Automation; Availability; Classificació INSPEC; Computer science; control theory; systems; Configuration space; Control system synthesis; Control theory. Systems; Decomposition; Dinàmica; Drives; Dynamics; Exact sciences and technology; Informàtica; Joints; Kinematics; kinematics singularities; Linkage mechanisms, cams; Manipulators; Mathematics; Mechanical engineering. Machine design; Orbital robotics; parallel manipulators; Parallel robots; Platforms; redundant manipulators; Robot arms; robot design; Robot kinematics; Robotics; Robots; Robòtica; Service robots; Simulation; Singularities; Strata; Strategy; Trajectory; Àrees temàtiques de la UPC; Availability; Statistical process control; Singularity; Control chart; parallel manipulators; Redundancy; Parallel mechanism; Control synthesis; Topology; redundant manipulators; Robotics; Manipulator; Direct problem; kinematics singularities; Kinematics; Linkage mechanism; Stratification; robot design; Configuration space
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2009.2018970

There are only three 6-SPS parallel manipulators with triangular base and platform, i.e., the octahedral, the flagged, and the partially flagged, which are studied in this paper. The forward kinematics of the octahedral manipulator is algebraically intricate, while those of the other two can be solved by three trilaterations. As an additional nice feature, the flagged manipulator is the only parallel platform for which a cell decomposition of its singularity locus has been derived. Here, we prove that the partially flagged manipulator also admits a well-behaved decomposition, technically called a stratification, some of whose strata are not topological cells, however. Remarkably, the adjacency diagram of the 5-D and 6-D strata (which shows what 5-D strata are contained in the closure of a 6-D one) is the same as for the flagged manipulator. The availability of such a decomposition permits devising a redundant 7-SPS manipulator, combining two partially flagged ones, which admits a control strategy that completely avoids singularities. Simulation results support these claims.