Robust Procedures for Obtaining Assembly Contact State Extremal Configurations

Two important components in the selection of an admittance that facilitates force-guided assembly are the identification of: 1) the set of feasible contact states, and 2) the set of configurations that span each contact state, i.e., the extremal configurations. We present a procedure to automatically generate both sets from CAD models of the assembly parts. In the procedure, all possible combinations of principle contacts are considered when generating hypothesized contact states. The feasibility of each is then evaluated in a genetic algorithm based optimization procedure. The maximum and minimum value of each of the 6 configuration variables spanning each contact state are obtained by again using genetic algorithms. Together, the genetic algorithm approach, the hierarchical data structure containing the states, the relationships among the states, and the extremals within each state are used to provide a reliable means of identifying all feasible contact states and their associated extremal configurations

Admittance Selection for Force-guided Assembly of Polyhedral Parts in Single-point Contact

The selection of the proper admittance is important in achieving force-guided assembly. This paper identifies procedures for selecting the appropriate spatial admittance to achieve reliable force-guided assembly of polyhedral parts for single-point frictionless contact cases. Sets of conditions that are imposed on the admittance matrix for different types of single-point contact are presented. These conditions ensure that the motion that results from contact reduces part misalignment in the selected contact state. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reduction conditions at a finite number of contact configurations, then the admittance also satisfy the conditions at all intermediate configurations

Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

Admittance Selection for Planar Force-Guided Assembly for Single-Point Contact with Friction

This paper identifies procedures for selecting the appropriate admittance to achieve reliable planar force-guided assembly for single-point frictional contact cases. A set of conditions that are imposed on the admittance matrix is presented. These conditions ensure that the motion that results from contact reduces part misalignment. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reduction conditions at a finite number of contact configurations and a given coefficient of friction /spl mu//sub M/) then the admittance will also ensure that the conditions are satisfied at all intermediate configurations for all coefficients less than /spl mu//sub M/

Realization Of Point Planar Elastic Behaviors Using Revolute Joint Serial Mechanisms Having Specified Link Lengths

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified

Sufficient Conditions for Admittance to Ensure Planar Force-assembly in Multi-point Frictionless Contact

An important issue in the development of force guidance assembly strategies is the specification of an appropriate admittance control law. This paper identifies procedures for selecting the appropriate admittance to achieve reliable planar force-guided assembly for multi-point contact cases. Conditions that restrict the admittance behavior for each of the various types of two-point contact are presented. These conditions ensure that the motion that results from contact reduces part misalignment for each case. We show that, for bounded misalignments, if the conditions are satisfied for a finite number of contact configurations, the conditions ensure that force guidance is achieved for all configurations within the specified bounds

Sufficient Conditions Used in Admittance Selection for Planar Force-guided Assembly

Admittance control approaches show significant promise in providing reliable force-guided assembly. An important issue in the development of these approaches is the specification of an appropriate admittance control law. This paper identifies procedures for selecting the appropriate admittance to achieve reliable planar force-guided assembly for single-point contact cases. A set of conditions that are imposed on the admittance matrix is presented. These conditions ensure that the motion that results from contact reduces part misalignment. We show that for bounded misalignment, if the conditions are satisfied for a finite number of contact configurations, the system ensures that force guidance is achieved for all intermediate configurations

Efficient Contact State Graph Generation for Assembly Applications

An important aspect in the design of many automated assembly strategies is the ability to automatically generate the set of contact states that may occur during an assembly task. In this paper, we present an efficient means of constructing the set of all geometrically feasible contact states that may occur within a bounded set of misalignments (bounds determined by robot inaccuracy). This set is stored as a graph, referred to as an Assembly Contact State Graph (ACSG), which indicates neighbor relationships between feasible states. An ACSG is constructed without user intervention in two stages. In the first stage, all hypothetical primitive principle contacts (PPCs; all contact states allowing 5 degrees of freedom) are evaluated for geometric feasibility with respect to part-imposed and robot-imposed restrictions on relative positioning (evaluated using optimization). In the second stage, the feasibility of each of the various combinations of PPCs is efficiently evaluated, first using topological existence and uniqueness criteria, then using part-imposed and robot-imposed geometric criteria

Comments on “The Principal Axes Decomposition of Spatial Stiffness Matrices”

A significant amount of research has been directed toward developing a more intuitive appreciation of spatial elastic behavior. Results of these analyses have been described in terms of behavior decompositions and in terms of behavior centers. In a recent paper entitled “The Principal Axes Decomposition of Spatial Stiffness Matrices” by Chen et al. (IEEE Trans. Robot., vol. 31, no. 1, pp. 191-207), a decomposition of spatial stiffness was presented, and centers of stiffness and compliance were identified. The results presented in the paper have substantial overlap with previously published results and redefine previously used terms. The objective of this communication is to clarify the contributions of prior work and to standardize the terminology used in describing spatial elastic behavior

Multidirectional Compliance and Constraint for Improved Robotic Deburring. Part 2: Improved Bracing

This two-part paper presents a method for both improving the positioning capability and increasing the effective stiffness (bracing) of a robotic manipulator through multidirectional compliance and constraint. Improved positioning and improved bracing are attained through the effective use of multiple unilateral kinematic constraints in different directions. The companion paper identified how to specify the compliant characteristics of a manipulator so contact forces lead to deflections that eliminate positional misalignments and result in improved relative positioning through force guidance. In this part, we show that the characteristics beneficial to force guidance are the same characteristics that provide improved bracing when partially constrained by contact. Improved bracing is demonstrated in the context of workpart edge deburring