Ernesto Staffetti

Integration of planning and execution in force controlled compliant motion

This paper presents the compliant task generator: a new approach for the automatic conversion of a geometric path generated by a compliant path planner to a force based task specification for a compliant robot controller. Based on the geometric model of a moving object and its environment, a compliant path planner generates a set of six-dimensional positions x/sub 1...m/ and their corresponding contact formations CF/sub 1...n/. The compliant force controller, which executes a planned path under force feedback using the hybrid control paradigm, expects a desired force w/sub d/, velocity t/sub d/ and position x/sub d/ at each time-step, together with their force and velocity controlled subspaces W and T. To specify these controller primitives, we add information about the desired dynamic interaction between the moving object and its environment, in the form of the desired kinetic energy E/sub kin/ of the moving object and the potential energy E/sub pot/ in the contacts with the environment, together with the inertia and stiffness matrix M and S. We fully automated the conversion process of the compliant planner output together with the added information about the dynamic interaction, to a force based task specification. This eliminates the requirement of human intervention between the planning and execution phase. The presented approach applies to all compliant motions between polyhedral objects, and is verified in a real world experiment.

Kinestatic analysis of robot manipulators using the Grassmann-Cayley algebra

This paper presents a novel framework for studying the statics and the instantaneous kinematics of robot manipulators based on the Grassmann-Cayley algebra. This algebra provides a complete mathematical interpretation of screw theory, in which twist and wrench spaces are represented by means of the concept of extensor, and the reciprocity condition between twist and wrench spaces of partially constrained rigid bodies is reflected by its inherent duality. Kinestatic analysis of robot manipulators entails computing sums and intersections of the twist and wrench spaces of the composing kinematic chains which are carried out by means of the operators join and meet of this algebra. The Grassmann-Cayley algebra permits us to work at the symbolic level, that is, in a coordinate-free manner. Moreover, it has an explicit formula for the meet operator that gives closed-form expressions of twist and wrench spaces of robot manipulators. Besides being computationally advantageous, the resulting formalism is conceptually much closer to the way humans think about kinestatics than geometric and coordinate-dependent methods, and therefore provides a deeper insight into the kinestatics of robot manipulators.

On the Invariance of Manipulability Indices

This work discusses the invariance of local manipulability indices which are used to convert into a scalar the capability of a robotic device at a given configuration to perform a manipulation task. It is shown that they suffer from non-invariance in the sense that arbitrariness in the choice of the metric functions employed in their definition is unavoidable and they are not invariant under changes of the arbitrary choices introduced. Since there do not exist natural norms in the spaces of generalized forces and velocities, kinematic manipulability is neither an invariant concept nor a natural notion.

Analysis of rigid body interactions for compliant motion tasks using the Grassmann-Cayley algebra

This paper studies the statics and the instantaneous kinematics of a rigid body constrained to keep an arbitrary number of surface-surface contacts with a rigid static environment during its motion. These properties are analyzed under the frictionless assumption by modelling each contact with a kinematic chain that instantaneously gives the same motion freedom as the contact itself and by studying the resulting parallel chain using the Grassmann-Cayley algebra. With this algebra twists and wrenches can be expressed by means of extensors and operated using the join and meet operators. Moreover, the duality inherent in this algebra is used to reflect the reciprocity condition between possible twists and admissible wrenches between partially constrained rigid bodies.This paper studies the statics and the instantaneous kinematics of a rigid body constrained by one to six contacts with a rigid static environment. These properties are analyzed under the frictionless assumption by modeling each contact with a kinematic chain that, instantaneously, is statically and kinematically equivalent to the contact and studying the resulting parallel chain using the Grassmann-Cayley algebra. This algebra provides a complete interpretation of screw theory, in which twist and wrench spaces are expressed by means of the concept of extensor and its inherent duality reflects the reciprocity condition between possible twists and admissible wrenches of partially constrained rigid bodies. Moreover, its join and meet operators are used to compute sum and intersections of the twist and wrench spaces resulting from serial and parallel composition of motion constraints. In particular, it has an explicit formula for the meet operator that gives closed-form expressions of twist and wrench spaces of rigid bodies in contact. The Grassmann-Cayley algebra permits us to work at the symbolic level, that is, in a coordinate-free manner and therefore provides a deeper insight into the kinestatics of rigid body interactions.

Kinestatic Analysis of Serial and Parallel Robot Manipulators Using Grassmann-Cayley Algebra

In this paper the statics and the instantaneous kinematics of serial and parallel robot manipulators are studied. A projective interpretation of the concepts of twist, wrench, twist space and wrench space — based on the concept of extensor — is presented and a description of the dualistic relation between twist and wrench spaces of serial and parallel robot manipulators is given in terms of the Grassmann-Cayley algebra. The importance of this algebra is that its join and meet operators are very effective tools for joining and intersecting the linear subspaces involved in the kinestatic analysis of manipulators when they are represented by extensors.

A simple characterization of the infinitesimal motions separating general polyhedra in contact

We present a simple local geometric characterization of the configuration space of two polyhedra in contact that provides a representation of all infinitesimal motions that separate them. The polyhedra considered are general in the sense that they possibly have non-convex faces and arbitrary number of holes. The approach presented has two main advantages over former ones: 1) it only relies on the classical basic contacts between polyhedra, i.e. the vertex-face and edge-edge contacts; and 2) it does not require the focal decomposition of non-convexities into convex parts.

Automatic verification of contact states taking into account manipulator constraints

Compliant motion is required or desirable in many robotic tasks, especially assembly tasks. Both planning and execution of autonomous compliant motion requires the knowledge of contact states between parts in contact beforehand. Previous research has addressed automatic generation of contact states between rigid objects. However, not all such contact states can be possibly reached if a rigid object is attached to and moved by a manipulator due to the manipulator constraints. In this paper, we study the problem of finding feasible contact states between a polyhedral part A held by a manipulator with a fixed base and a fixed polyhedral part B. Given a contact state graph between the unattached part A and the fixed part B, our approach then attaches A to the manipulator model and checks the reachability of each contact state and the connection between two neighboring contact states by applying a virtual compliant controller to the manipulator to test possible compliant motions of A. Implementation results validate the effectiveness of our method.

Shape Representation and Indexing Based on Region Connection Calculus and Oriented Matroid Theory

In this paper a novel method for indexing views of 3D objects is presented. The topological properties of the regions of the views of a set of objects are used to define an index based on the region connection calculus and oriented matroid theory. Both are formalisms for qualitative spatial representation and reasoning and are complementary in the sense that whereas the region connection calculus encodes information about connectivity of pairs of connected regions of the view, oriented matroids encode relative position of the disjoint regions of the view and give local and global topological information about their spatial distribution. This indexing technique is applied to 3D object hypothesis generation from single views to reduce candidates in object recognition processes.

A New Formalism to Characterize Contact States Involving Articulated Polyhedral Objects

In this paper a novel formalism to characterize contact states between an articulated polyhedral object and a polyhedral environment for the generation of the graph of feasible contact states between them is presented. This formalism is based upon a particular representation of the stratification of the configuration space of the articulated object by means of oriented matroid theory. A stratification is a decomposition of a set into a collection of manifolds which in our case correspond to the different contact states between the articulated object and the environment. In the representation of the stratification of the configuration space using oriented matroid theory the topological properties of the different strata are represented at a purely combinatorial level. An algorithm to enumerate the existing strata and to find the adjacency relationships among them is proposed. It will be shown that the symbolic computation based on oriented matroids simplifies and in some cases even replaces the computation with coordinates.

Planar contour tracking in the presence of pose and model errors by Kalman filtering techniques

The paper presents a solution to the problem of planar contour tracking with a force-controlled robot. The contour shape is unknown and is characterized at each time step by the curvature together with the orientation angle and arc length. The unknown continuously changing contour curvature is supposed to be within a preliminary given interval. An interacting multiple model (IMM) filter is implemented to cope with the uncertainties. The interval of possible curvature values is discretized. i.e., a grid is formed and several extended Kalman filters (EKFs) are running in parallel. The curvature estimate represents a fusion of the values from the grid with the IMM probabilities. The orientation angle estimate is also a fusion of the estimates, obtained from the separate Kalman filters with the mode probabilities. A single extended Kalman filter is implemented to localize the unknown initial robot end-effector position over the contour. The performance of both algorithms is investigated and the results based on real data are presented.