Special purpose compliant end-effectors are effective in realizing task-appropriate passive compliance. This paper presents a programmable, 3 -fingered, antagonistic, compliant hand (P3ACH) capable of realizing a desired compliant behavior within a large space of multidirectional compliant behaviors. Manipulation dexterity is demonstrated by performing different assembly tasks faster, more robustly, and with lower contact forces than an active system realizing the same compliant behavior.

This article identifies the space of spatial impedance behaviors that can be achieved by a grasp of a multifinger hand in which each fingertip makes hard-point contact with the held object. The dimension of the space of realizable impedances for a given number of fingers is determined analytically. A set of necessary and sufficient conditions on impedance matrices that can be realized by a given grasp is developed and the physical significance of these conditions is identified. The space of impedances that can be achieved by a hard point grasp is a hyperplane in the space of all possible impedance behaviors. A process to achieve an arbitrary full-rank impedance in the hyperplane with a grasp having the minimum number of fingers is developed. With this process, any spatial impedance behavior in the hyperplane can be attained with a three-finger grasp by properly selecting: first, the locations where fingertips contact the held object, and second, the translational impedance provided by a finger at each of these locations.

This paper presents the design and performance of a planar 3R robot capable of dexterous constrained manipulation when interacting with a stiff environment. A novel variable stiffness actuator (VSA) having a stiffness ratio of approximately 500 is also described. Variable stiffness actuation, together with a combined position/compliance manipulation path, is used to: 1) allow the robot to passively comply with its environment along kinematically constrained directions despite model error in constraint locations, and 2) generate high stiffness for accurate motion control along kinematically unconstrained directions despite resisting forces. This manipulation strategy provides dexterity for cases in which mechanical work must be performed while complying with constraints. The manipulation strategy and robot performance were evaluated with the task of turning a steel crank to lift a weight. Results show that, when using passive compliance control, the robot completed the task 29 times faster with constraint forces 80% lower than when using traditional active compliance control (with VSAs at their highest stiffness).

This paper identifies conditions for designing the appropriate spatial admittance to achieve reliable force-guided assembly of polyhedral parts for cases in which a single frictional contact occurs between the two parts. This work is an extension of previous work in which frictionless contact was considered. This paper presents a way to characterize friction without solving a set of complicated non-linear equations. We show that, by modifying the error reduction function and evaluating the function bounds associated with friction, the procedures developed for frictionless contact apply to the frictional cases. Thus, for bounded misalignments, if an admittance satisfies the misalignment-reducing conditions at a finite number of contact configurations, then the admittance will also satisfy the conditions at all intermediate configurations for any value of friction less than the specified upper bound.

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.

The high stiffness of conventional robots is beneficial in attaining highly accurate positioning in free space. High stiffness, however, limits a robot's ability to perform constrained manipulation. Because of the high stiffness, geometric conflict between the robot and task constraints during constrained manipulation can lead to excessive forces and task failure. Variable stiffness actuators can be used to adjust the stiffness of robot joints to allow high stiffness in unconstrained directions and low stiffness in constrained directions. Two important design criteria for variable stiffness actuation are a large range of stiffness and a compact size. A new design, the Arched Flexure VSA, uses a cantilevered beam flexure of variable cross-section and a controllable load location. It allows the joint to have continuously variable stiffness within a finite stiffness range, have zero stiffness for a small range of joint motion, and allow rapid adjustment of stiffness. Using finite element analysis, flexure geometry was optimized to achieve high stiffness in a compact size. A proof-of-concept prototype demonstrated continuously variable stiffness with a ratio of high stiffness to low stiffness of 55.

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 behaviordecompositionsand in terms of behaviorcenters. In a recent paper entitled “The Principal Axes Decomposition of Spatial Stiffness Matrices” by Chenet 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.

Robots are not typically used for assembly tasks in which positioning requirements exceed robot capabilities. To address this limitation, a significant amount of work has been directed toward identifying desirable mechanical behavior of a robot for force-guided assembly. Most of this work has been directed toward the `standard' peg-in-hole assembly problem. Little has been done to identify the specific behavior necessary for reliable assembly for different types of polygonal parts, and little has been done relating assembly characteristics to classes of part geometries. This paper presents the best passive admittance and associated maximum coefficient of friction for planar force-assembly of a variety of different polygonal parts, specifically pegs with rectangular, trapezoidal, triangular, and pentagonal cross sections. The results show that force-guided assembly can be reliably achieved at higher values of friction when parts are shorter and wider. For all geometries considered, force-guided assembly is ensured for any value of friction less than 0.8 when the optimal admittance is used; and, for some geometries, for any value of friction less than 15.

The admittance of a manipulator can be used to improve robotic assembly. If properly selected, the admittance will regulate a contact force and use it to guide the parts to proper positioning. In previous work, procedures for selecting the appropriate admittance for single principal contact (PC) cases were identified. This paper extends this research for some of the two PC cases-those for which each contact occurs at a single point. The conditions obtained ensure that the motion that results from frictionless contact always instantaneously reduces part misalignment. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reducing conditions at a finite number of contact configurations, then the admittance will also satisfy the conditions at all intermediate configurations.

By judiciously selecting the admittance of a manipulator, the forces of contact that occur during assembly can be used to guide the parts to proper positioning. This paper identifies conditions for selecting the appropriate spatial admittance to achieve reliable force-guided assembly of polyhedral parts for cases in which a single feature (vertex, edge, or face) of one part contacts a single feature of the other, i.e., all single principal contact cases. These conditions ensure that the motion that results from frictionless contact always instantaneously reduces part misalignment. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reducing conditions at a finite number of contact configurations, then the admittance will also satisfy the conditions at all intermediate configurations.

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.

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.

An important issue in the development of force guidance assembly strategies is the specification of an appropriate admittance control law. This paper identifies conditions to be satisfied when selecting the appropriate admittance to achieve force-guided assembly of polygonal parts for multipoint contact with friction. These conditions restrict the admittance behavior for each of the various one-point and two-point contact cases and ensure that the motion that results from contact reduces part misalignment for each case. We show that, for bounded friction and part misalignments, if the identified conditions are satisfied for a finite number of contact configurations and friction coefficients, the conditions ensure that force guidance is achieved for all configurations and values of friction within the specified bounds.

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/.

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.

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.

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 force-guided assembly of planar polyhedral parts 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 misalignments, if an admittance satisfies the misalignment-reduction conditions at a finite number of contact configurations, then the admittance will also satisfy the conditions at all intermediate configurations.

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.

We address the spatial elastic behavior that can be achieved through the use of a serial chain of revolute and prismatic elastic joints. We show that, regardless of the number of joints or the configuration of the links, there exists a subspace within the 21-dimensional compliance matrix space that cannot be reached by a simple serial elastic mechanism. This restriction is shown to be dual to the restriction on the stiffness matrices associated with simple parallel mechanisms. Although analogous to each other, the two restrictions correspond to different elastic behaviors. A procedure to synthesize any realizable compliance matrix with a simple serial mechanism is provided. The dualities and differences between the parallel and serial cases are discussed.

We address the spatial elastic behavior that can be achieved through the use of a serial chain of revolute and prismatic elastic joints. We show that, regardless of the number of joints or the configuration of the links, there exists a subspace within the 21-dimensional compliance matrix space that cannot be reached by a simple serial elastic mechanism. This restriction is shown to be dual to the restriction on the stiffness matrices associated with simple parallel mechanisms. Although analogous to each other, the two restrictions correspond to different elastic behaviors. A procedure to synthesize any realizable compliance matrix with a simple serial mechanism is provided. The dualities and differences between the parallel and serial cases are discussed.

A manipulator system is modeled as a kinematically unconstrained rigid body suspended by elastic devices. The structure of spatial stiffness is investigated by evaluating the stiffness matrix "primitives"-the rank-1 matrices that compose a spatial stiffness matrix. Although the decomposition of a rank-2 or higher stiffness matrix into the sum of rank-1 matrices is not unique, one property of the set of matrices is conserved. This property, defined as the stiffness-coupling index, identifies how the translational and rotational components of the stiffness are related. Here, we investigate the stiffness-coupling index of the rank-1 matrices that compose a spatial stiffness matrix. We develop a matrix decomposition that yields a set of rank-1 stiffness matrices that identifies the bounds on the stiffness-coupling index for any decomposition. This decomposition, referred to as the eigenscrew decomposition, is shown to be invariant in coordinate transformation. With this decomposition, we provide some physical insight into the behavior associated with a general spatial stiffness matrix.

In this paper, the structure and extremal properties of spatial stiffness matrices are investigated. From this work a better understanding of the spatial compliant behavior important in robot interaction tasks is attained. We develop a rank-1 decomposition of a spatial stiffness matrix which is independent of the coordinate frame used to describe the elastic behavior. We also identify the extremal properties associated with this decomposition. To attain better physical insight, analogies are drawn between this unique spatial stiffness matrix decomposition and the conventional eigenvalues decomposition of a translational stiffness matrix.

We identify the space of spatial compliant behavior that can be achieved through the use of simple springs connected in parallel to a single rigid body. Here, the expression "simple spring" refers to the set of compliant relations associated with passive translational springs and rotational springs. The restriction on the stiffness matrices is derived using the screw theory by investigating the compliant behavior of individual simple springs. We show that the restriction results from the fact that simple springs can only provide either a pure force or a pure torque to the suspended body. We show that the 20-dimensional subspace of "realizable" spatial stiffness matrices achieved with parallel simple springs is defined by a linear necessary and sufficient condition on the positive semidefinite stiffness matrix. A procedure to synthesize an arbitrary full-rank stiffness matrix within this realizable subspace is provided. This procedure requires no more than seven simple springs.

Force-assembly has been defined as an assembly process for which the use of a single, properly designed, admittance control law will guarantee the proper assembly of a given pair of mating parts. In previous work in workpart-into-fixture insertion, the conditions on a manipulators accommodation control law that ensure proper insertion despite infinitesimal positional error and finite (but bounded) friction have been identified. Through the use of an optimization routine, a control law that satisfies these force-assembly conditions at or below a friction maximum value can be obtained. This single control law, however, is not unique-there exists many other control laws that will satisfy the conditions of force-assembly at the same value of friction. This paper addresses the identification and construction of a linear space of accommodation control law parameters that ensure force-assembly with friction. First, linear sufficient conditions that ensure force-assembly with friction are identified. These linear sufficient conditions are then modified to separate the N/sup 2/+N dimensional space of accommodation control law parameters into N+1 different N-dimensional subspaces. A means of efficiently generating basis nominal velocity vectors and basis accommodation matrices is presented. A nominal velocity selected using any positive linear combination of the nominal velocity basis vectors and an accommodation matrix selected using any positive linear combination of the accommodation basis matrices will guarantee force-assembly (for any value of friction less than that used in generating the basis matrices). A planar example of the construction of each accommodation control law subspace is presented and illustrated in the geometry of the fixturing task.

In this paper, a method for accurate positioning using compliance and constraint is applied to material removal processes. Accurate force guidance is achieved through the use of an end-effector mounted jig in conjunction with the proper design of the compliance of the manipulator and the material removal tool. The compliance of the manipulator is designed so that: 1) an initial unique relative position/orientation of the jig with respect to the workpart edge is attained despite manipulator positioning error; and 2) the unique relative position initially established is maintained while moving along the workpart edge. Also, the stiffness of the material removal tool is regulated to ensure that forces associated with material removal do not degrade the accuracy of jig-assisted force guided manipulator positioning. This work has application in material removal processes in which accurate positioning with respect to an edge is important, e.g., robotic deburring and aircraft panel drilling. Conditions on the manipulator compliance also have application in robotic assembly.>

Previously, force-assembly has been defined as an assembly process for which a single admittance control law (i.e., a single nominal velocity in conjunction with a single mapping of forces to motions) can guarantee the proper assembly of a given pair of mating parts. As a testbed application of force-assembly, the insertion of a workpiece into a fixture consisting of multiple rigid fixture elements (fixels) is addressed. Previous work in this area has shown that, when workpiece/fixture contact is frictionless and positional error is infinitesimal, there always exists an admittance control law that will ensure the proper insertion of a workpiece into a deterministic fixture. When workpiece/fixture contact is frictionless, the workpiece/fixture contact force contains the relative positional information required to identify error-reducing motions. Friction between the workpiece and fixture, however, provides a disturbance to the geometrical information contained in the contact force. This paper addresses: 1) the identification of the conditions that must be satisfied for force-assembly with friction, and 2) the formulation and results of an optimization of the admittance control law to obtain the maximum value of friction that will satisfy the force-assembly conditions for a given workpiece/fixture combination. Results indicate that force-assembly fails when the contact forces are no longer characteristic. Forces are characteristic if the possible contact forces that may occur for one type of misalignment are unique to that type of misalignment.>

The design of an admittance control law for reliable force-guided assembly is addressed. The overall objective is to design the manipulator's mechanical performance so that, at each possible bounded part misalignment, the contact force always leads to a motion that alleviates the misalignment. The implementation of such an approach using a single nominal velocity and a single admittance function is referred to as force-assembly. Previous work addressing force-assembly of a workpiece into a fixture has shown that when workpiece/fixture contact is frictionless there always exists an admittance control law that ensures the proper insertion of a workpiece into a deterministic future. The authors discuss the identification of the condition that must be satisfied for force-assembly with friction and the optimization of the admittance control law to obtain the maximum value of friction that satisfies the force-assembly conditions for a given workpiece-fixture combination.>

The authors address the design of manipulator admittance for reliable force-guided assembly. Their goal is to design the admittance of the manipulator so that, at all possible bounded part misalignments, the contact forces always lead to error-reducing motions. If this objective can be accomplished for a given pair of mating parts, the parts are called force-assemblable. As a testbed application of manipulator admittance design for force-guided assembly, the authors investigate the insertion of a workpiece into a fixture consisting of multiple rigid fixture to be one for which there exists an admittance matrix that ensures the unique positioning of a workpiece despite initial positional error. It is shown that, in the absence of friction, all deterministic fixtures are linearly force-assemblable. How to design an admittance matrix that guarantees that the workpiece will be guided into the deterministic fixture by the fixel contact forces alone is shown.>

The authors describe the concept of force-assemblability, which may be applied to fixture insertion as well as other assembly tasks. They define a linear force assemblable fixture to be one for which there exists a linear motion control law (examples of which include compliance and accommodation) which necessarily results in workpiece contact with all fixture elements (fixels) despite initial positional error. For reliable insertion, the fixture should have the property that contact with all fixels insures a unique workpiece position (i.e. the fixture should be deterministic) and the property that, after the inserting motion terminates, contact with all fixels is insured. It is shown that all deterministic fixtures are force-assemblable when friction is less than some value dictated by the workpiece/fixture geometry. It is also shown how to generate a motion control law that satisfies force-assemblability at this value of friction.>

A methodology is described by which erroneous contact configurations for a given task are used to synthesize an appropriate accommodation matrix (either diagonal or nondiagonal) such that the motions which result from contact with the environment are error corrective. The methodology is verified by the synthesis and experimental validation of a nondiagonal accommodation matrix sufficient for an error-corrective place-in-detent robotic assembly operation, an operation that fails if a diagonal accommodation matrix is used.>