This paper presents an iterative learning control method for precise aircraft trajectory tracking. Given a trajectory to be followed by an aircraft with a dynamical model which is assumed to be known, the proposed algorithm improves the system performance in following the trajectory using the spatial and temporal deviations suffered by previous flights to anticipate recurring disturbances and compensate for them proactively by generating a new reference trajectory to be followed, which is the input for the aircraft’s own trajectory tracking controller. The proposed method is tested in a simulated busy terminal maneuvering area in which the time-based separation between aircraft is short enough for similar weather conditions to be expected. The numerical experiments are conducted considering aircraft of the same type, which are assumed to follow the same trajectory in two operations in which precise trajectory tracking is essential: continuous climb and descent operations. The obtained results show a significant reduction of the trajectory tracking error in few iterations, proving the effectiveness of the iterative learning control method applied to commercial aircraft trajectory tracking. Higher precision in trajectory tracking implies higher predictability of aircraft trajectories, which results in an improvement of the efficiency and capacity of the air traffic management system and in reductions of costs and emissions.

Robot programming by demonstration is a robot programming paradigm in which a human operator directly demonstrates the task to be performed. In this paper, we focus on programming by demonstration of compliant motion tasks, which are tasks that involve contacts between an object manipulated by the robot and the environment in which it operates. Critical issues in this paradigm are to distinguish essential actions from those that are not relevant for the correct execution of the task and to transform this information into a robot-independent representation. Essential actions in compliant motion tasks are the contacts that take place, and therefore, it is important to understand the sequence of contact states that occur during a demonstration, called contact classification or contact segmentation. We propose a contact classification algorithm based on a supervised learning algorithm, in particular on a stochastic gradient boosting algorithm. The approach described in this paper is accurate and does not depend on the geometric model of the objects involved in the demonstration. It neither relies on the kinestatic model of the contact interactions nor on the contact state graph, whose computation is usually of prohibitive complexity even for very simple geometric object models.

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.

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.

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.

Information of high-level, topological contact states is useful and even necessary for a wide range of applications, including many robotic applications. A contact state between two polyhedral objects can be effectively represented as a contact formation in terms of a set of principal contacts between faces, edges, and vertices of the two objects. However, little is done to characterize and represent contact states between curved objects. In order to facilitate the representation of contact states between such objects, we introduce a novel approach to segment the boundary of curved objects based on monotonic changes of curvatures, which we call the curvature monotonic segmentation. We specifically apply this approach to curved 2D and 3D objects with boundary curves or surfaces represented by algebraic polynomials of degrees up to 2. The segmentation yields curvature monotonic faces and edges (or pseudo edges), and vertices (or pseudo vertices). With these faces, (pseudo) edges, and (pseudo) vertices, we effectively extend the concept of contact formation to curved objects to represent high-level, topological contact states between such objects with the same desirable characteristics as the contact formations between polyhedral objects.

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.

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.

An analytic formulation of the statics and the instantaneous kinematics of robot manipulators based on Grassmann-Cayley algebra is presented. The notions of twist, wrench, twist space and wrench space are mathematically represented by the concept of extensors of this algebra and the reciprocity relation between twist and wrench spaces of partially constrained rigid bodies is reflected by its inherent duality. Kinestatic analysis of manipulators implies the computation of sums and intersections of the twist and wrench spaces of the composing chains which are carried out by means of the join and meet operators of this algebra when the linear subspaces involved in the kinestatic analysis of manipulators are represented by extensors. The importance of Grassmann-Cayley algebra in kinestatics is that it has an explicit formula for the meet operator that gives analytical expressions of the twist and wrench space of robot manipulators with arbitrary topology.

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.

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.

The computation of linear moment matrices, whose elements are defined as zeroth order integration values of an image, was recently introduced as a tool to reduce the computational cost required to obtain the geometric moments of an image. The main relevance of these matrices is twofold: on one hand, they can be efficiently obtained by means of accumulation filters, which only require additions; on the other one, their relation to geometric moments, as well as to discrete Fourier spectrum coefficients, allows the exchange and interpretation of many results from different areas of image processing and pattern recognition. Taking into account the relevance of these matrices, a new recursive property that allows their efficient computation in sliding-window processes is presented here. First, a scalar recursive updating rule is formulated. It relates the value of each element of a linear moment matrix to those calculated in the previous location of the sliding-window. Then, this result is reformulated to obtain an explicit matrix formula. The obtained recursive updating rule has a straightforward application in many different fields involving sliding window processes in order to efficiently obtain local features related to geometric moments and discrete Fourier spectrum coefficients.