Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack-to keep the control of the robot-nor excessively tightto prevent cable breakage-even in the presence of bounded perturbations of the wrench. This paper proposes a path-planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The configuration space, or C-space for short, is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path nonexistence is proved by exhaustion of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose or to synthesize free-flying motions in the full 6-D C-space. Experiments illustrate the performance of the method in a real prototype.
Rozo, L.; Calinon, .; Caldwell, D.; Jimenez, P.; Torras, C. IEEE journal of robotics and automation Vol. 32, num. 3, p. 513-527 DOI: 10.1109/TRO.2016.2540623 Data de publicació: 2016-04-01 Article en revista
Robots are becoming safe and smart enough to work alongside people not only on manufacturing production lines, but also in spaces such as houses, museums, or hospitals. This can be significantly exploited in situations in which a human needs the help of another person to perform a task, because a robot may take the role of the helper. In this sense, a human and the robotic assistant may cooperatively carry out a variety of tasks, therefore requiring the robot to communicate with the person, understand his/her needs, and behave accordingly. To achieve this, we propose a framework for a user to teach a robot collaborative skills from demonstrations. We mainly focus on tasks involving physical contact with the user, in which not only position, but also force sensing and compliance become highly relevant. Specifically, we present an approach that combines probabilistic learning, dynamical systems, and stiffness estimation to encode the robot behavior along the task. Our method allows a robot to learn not only trajectory following skills, but also impedance behaviors. To show the functionality and flexibility of our approach, two different testbeds are used: a transportation task and a collaborative table assembly.
Fomin, V.M.; Hippler, M.; Magdanz, V.; Soler, L.; Sanchez, S.; Schmidt, O.G. IEEE journal of robotics and automation Vol. 30, num. 1, p. 40-48 DOI: 10.1109/TRO.2013.2283929 Data de publicació: 2014-02-05 Article en revista
We describe the propulsion mechanism of the catalytic microjet engines that are fabricated using rolled-up nanotech. Microjets have recently shown numerous potential applications in nanorobotics but currently there is a lack of an accurate theoretical model that describes the origin of the motion as well as the mechanism of self-propulsion. The geometric asymmetry of a tubular microjet leads to the development of a capillary force, which tends to propel a bubble toward the larger opening of the tube. Because of this motion in an asymmetric tube, there emerges a momentum transfer to the fluid. In order to compensate this momentum transfer, a jet force acting on the tube occurs. This force, which is counterbalanced by the linear drag force, enables tube velocities of the order of 100 µm/s. This mechanism provides a fundamental explanation for the development of driving forces that are acting on bubbles in tubular microjets.
Dual quaternions give a neat and succinct way to encapsulate both translations and rotations into a unified representation that can easily be concatenated and interpolated. Unfortunately, the combination of quaternions and dual numbers seem quite abstract and somewhat arbitrary when approached for the first time. Actually, the use of quaternions or dual numbers separately are already seen as a break in mainstream robot kinematics, which is based on homogeneous transformations. This paper shows how dual quaternions arise in a natural way when approximating 3D homogeneous transformations by 4D rotation matrices. This results in a seamless presentation of rigid-body transformations based on matrices and dual quaternions which permits building intuition about the use of quaternions and their generalizations.
Bohigas, O.; Zlatanov, D.; Ros, L.; Manubens, M.; Porta, J. IEEE journal of robotics and automation Vol. 30, num. 2, p. 340-351 DOI: 10.1109/TRO.2013.2283416 Data de publicació: 2014 Article en revista
The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.
This paper presents a proportional plus damping controller that can asymptotically drive a network composed of N nonidentical Euler-Lagrange (EL) systems toward a consensus point. The agents can be fully actuated or can belong to a class of underactuated EL-systems. The network is modeled as a weighted and undirected static interconnection graph that can exhibit asymmetric variable time delays. Simulations, using a network with ten EL-systems, are reported to support the theoretical contributions of this study.
The real roots of the univariate polynomial closure condition of a planar parallel robot determine the solutions of its forward kinematics. This paper shows how the univariate polynomials of all fully parallel planar robots can be derived directly from that of the widely known 3-RPR robot by simply formulating these polynomials in terms of distances and oriented areas. This is a relevant result because it avoids the case-by-case treatment that requires different sets of variable eliminations to obtain the univariate polynomial of each fully parallel planar robot.
This paper demonstrates that for certain choices of mass distribution and addition of springs, an underactuated two-degree-of-freedom (2-DOF) P RRRP system is static feedback linearizable, i.e., differentially flat as well. This paper is original and provides a ground breaking study in
underactuated dynamical systems.
This paper presents a procedure for synthesizing high-quality grasps for objects that need to be held and manipulated in a specific way, characterized by a prespecified set of contact constraints to be satisfied. Due to the multimodal nature of typical grasp quality measures, approaches that resort to local optimization methods are likely to get trapped into local extrema on such a problem. An additional difficulty is that the set of feasible grasps is a highly dimensional manifold, implicitly defined by a system of nonlinear equations. The proposed procedure finds a way around these issues by focusing the exploration on a relevant subset of grasps of lower dimension and tracing this subset exhaustively using a higher-dimensional continuation technique. A detailed atlas of the subset is obtained as a result, on which the highest quality grasp, according to any desired criterion, or a combination of criteria, can be readily identified. Examples are included that illustrate the application of the method to a three-fingered planar hand and to the Schunk anthropomorphic hand grasping different objects, using several quality indices.
This paper presents a procedure to synthesize highquality grasps for objects that need to be held and manipulated
in a specific way, characterized by a pre-specified set of contact constraints to be satisfied. Due to the multi-modal nature of typical grasp quality measures, approaches that resort to local optimization methods are likely to get trapped into local extrema on such problem. An additional difficulty of the problem is that the set of feasible grasps is a highly-dimensional manifold, implicitly defined by a system of non-linear equations. The proposed procedure finds a way around these issues by focusing
the exploration on a relevant subset of grasps of lower dimension, and tracing this subset exhaustively using a higher-dimensional continuation technique. A detailed atlas of the subset is obtained
as a result, on which the highest-quality grasp according to any desired criterion, or a combination of criteria, can be readily
identified. Examples are included that illustrate the application of the method to a three-fingered planar hand and to the Schunk anthropomorphic hand grasping several objects, using several quality indices.
The situation arising in path planning under kinematic constraints, where the valid configurations define a manifold embedded in the joint ambient space, can be seen as a limit case of the well-known narrow corridor problem. With kinematic constraints, the probability of obtaining a valid configuration by sampling in the joint ambient space is not low but null, which complicates the direct application of sampling-based path planners. This paper presents the AtlasRRT algorithm, which is a planner especially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize a manifold and to coordinate the charts, forming an atlas that fully covers it. AtlasRRT simultaneously builds an atlas and a bidirectional rapidly exploring random tree (RRT), using the atlas to sample configurations and to grow the branches of the RRTs, and the RRTs to devise directions of expansion for the atlas. The efficiency of AtlasRRT is evaluated in several benchmarks involving high-dimensional manifolds embedded in large ambient spaces. The results show that the combined use of the atlas and the RRTs produces a more rapid exploration of the configuration space manifolds than existing approaches.
Bohigas, O.; Henderson, M.; Ros, L.; Manubens, M.; Porta, J. IEEE journal of robotics and automation Vol. 29, num. 4, p. 888-898 DOI: 10.1109/TRO.2013.2260679 Data de publicació: 2013 Article en revista
This paper provides an algorithm for computing singularity-free paths on closed-chain manipulators. Given two
non-singular configurations of the manipulator, the method attempts to connect them through a path that maintains a
minimum clearance with respect to the singularity locus at all points, which guarantees the controllability of the manipulator everywhere along the path. The method can be applied to non-redundant manipulators of general architecture, and it is resolution-complete. It always returns a path whenever one exists at a given resolution, or determines path non-existence
otherwise. The strategy relies on defining a smooth manifold that maintains a one-to-one correspondence with the singularity-free
C-space of the manipulator, and on using a higher-dimensional continuation technique to explore this manifold systematically from one configuration, until the second configuration is found.
If desired, the method can also be used to compute an exhaustive atlas of the whole singularity-free component reachable from a
given configuration, which is useful to rapidly resolve subsequent planning queries within such component, or to visualize the
singularity-free workspace of any of the manipulator coordinates.
Examples are included that demonstrate the performance of the method on illustrative situations.
The maps that are built by standard feature-based simultaneous localization and mapping (SLAM) methods cannot be directly used to compute paths for navigation, unless enriched with obstacle or traversability information, with the consequent increase in complexity. Here, we propose a method that directly uses the Pose SLAM graph of constraints to determine the path between two robot configurations with lowest accumulated pose uncertainty, i.e., the most reliable path to the goal. The method shows improved navigation results when compared with standard path-planning strategies over both datasets and real-world experiments.
This paper introduces a new method for workspace boundary determination on general structure manipulators. The method uses a branch-and-prune technique to isolate a set of output singularities and then classifies the points on such a set according to whether they correspond to motion impediments in the workspace. A detailed map of the workspace is obtained as a result, where all interior and exterior regions, together with the singularity and barrier sets that separate them, get clearly identified. The method can deal with open- or closed-chain manipulators, whether planar or spatial, and is able to take joint limits into account. Advantages over previous general methods based on continuation include the ability to converge to all boundary points, even in higher dimensional cases, and the fact that manual guidance with a priori knowledge of the workspace is not required. Examples are included that show the performance of the method on benchmark problems documented in the literature, as well as on new ones unsolved so far.
The algebraic characterization of the singularities of a Stewart platform is usually presented as a 6 × 6 determinant,
whose rows correspond to the line coordinates of its legs, equated to zero. This expression can be rewritten in a more amenable way, known as the pure condition, as sums and products of 4×4 determinants whose rows correspond to the point coordinates of the legs attachments. Researchers usually rely on one of these
two expressions to find the geometric conditions associated with the singularities of a particular Stewart platform. Although both are equivalent, it is advantageous to use either line or point coordinates depending on the platform topology. In this context, an equivalent expression involving only plane coordinates, a dual expression to that using point coordinates, seems to be missing.
This paper is devoted to its derivation and to show how its use is advantageous in many practical cases mainly because of its surprising simplicity: it only involves the addition of 4 × 4 determinants whose rows are plane coordinates defined by sets of three attachments.
A 5-SPU robot with collinear universal joints is well
suited to handling an axisymmetric tool, since it has 5 controllable
DoFs and the remaining one is a free rotation around the tool. The
kinematics of such a robot having also coplanar spherical joints
has previously been studied as a rigid subassembly of a Stewart-
Gough platform, it being denoted a line-plane component. Here
we investigate how to move the leg attachments in the base and
the platform without altering the robot’s singularity locus. By
introducing the so-called 3D space of leg attachments, we prove
that there are only three general topologies for the singularity
locus corresponding to the families of quartically-, cubicallyand
quadratically-solvable 5-SPU robots. The members of the
last family have only 4 assembly modes, which are obtained
by solving two quadratic equations. Two practical features of
these quadratically-solvable robots are the large manipulability
within each connected component and the fact that, for a fixed
orientation of the tool, the singularity locus reduces to a plane.
The standard forward kinematics analysis of 3-RPR planar parallel robots boils down to computing the roots of a sextic polynomial.
There are many different ways to obtain this polynomial but most of them include exceptions for which the formulation is not valid. Unfortunately, near these exceptions the corresponding polynomial exhibits numerical instabilities. In this paper, we provide a way around this inconvenience
by translating the forward kinematics problem to be solved into an equivalent problem fully stated in terms of distances. Using constructive geometric arguments, an alternative sextic —which is not linked to
a particular reference frame— is straightforwardly obtained without the need of variable eliminations nor tangent-half-angle substitutions. The presented formulation is valid, without any modification, for any planar 3-RPR parallel robot, including the special architectures and configurations —which ultimately lead to numerical instabilities— that cannot be directly handled by previous formulations.
This paper addresses path planning to consider a cost function defined over the configuration space. The proposed planner
computes low-cost paths that follow valleys and saddle points of the configuration-space costmap. It combines the exploratory
strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states. The planner is analyzed and shown to compute low-cost solutions with respect to a path-quality criterion based on the notion of mechanical work. A large set of experimental results is provided to demonstrate the effectiveness of the method. Current limitations and possible extensions are also discussed.
Pose SLAMis the variant of simultaneous localization and map building (SLAM) is the variant of SLAM, in which only the robot trajectory is estimated and where landmarks are only used to produce relative constraints between robot poses. To reduce
the computational cost of the information filter form of PoseSLAM and, at the same time, to delay inconsistency as much as possible, we introduce an approach that takes into account only highly informative
loop-closure links and nonredundant poses. This approach includes constant time procedures to compute the distance between
poses, the expected information gain for each potential link, and the exact marginal covariances while moving in open loop, as well as a procedure to recover the state after a loop closure that, in practical
situations, scales linearly in terms of both time and memory. Using these procedures, the robot operates most of the time in open loop,
and the cost of the loop closure is amortized over long trajectories. This way, the computational bottleneck shifts to data association, which is the search over the set of previously visited poses to determine
good candidates for sensor registration. To speed up data association, we introduce a method to search for neighboring poses
whose complexity ranges from logarithmic in the usual case to linear in degenerate situations. The method is based on organizing
the pose information in a balanced tree whose internal levels are defined using interval arithmetic. The proposed Pose-SLAM
approach is validated through simulations, real mapping sessions, and experiments using standard SLAM data sets.
Any set of two legs in a Gough-Stewart platform sharing an attachment is defined as a Delta component. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a Delta component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Gough-Stewart platform remains the same, provided that no architectural singularities are introduced. Such leg rearrangements are defined as Delta-transforms, and they can be applied sequentially and simultaneously. Although it may seem counterintuitive at first glance, the rearrangement of legs using simultaneous Delta-transforms does not necessarily lead to leg configurations containing a Delta component. As a consequence, the application of Delta-transforms reveals itself as a simple, yet powerful, technique for the kinematic analysis of large families of Gough-Stewart platforms. It is also shown that these transforms shed new light on the characterization of architectural singularities and their associated self-motions.
Anyset of two legs in a Gough–Stewart platform sharing an attachment is defined as a Δcomponent. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a Δ component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Gough–Stewart platform remains the same, provided that no architectural singularities are introduced. Such leg rearrangements are defined as Δ-transforms, and they can be applied sequentially and simultaneously. Although it may seem counterintuitive at first glance, the rearrangement of legs using simultaneous Δ-transforms does not necessarily lead to leg configurations containing a Δcomponent. As a consequence, the application of Δ-transforms reveals itself as a simple, yet powerful, technique for the kinematic analysis of large families of Gough–Stewart platforms. It is also shown that these transforms shed new light on the characterization of architectural singularities and their associated self-motions.
There are only three 6-SPS parallelmanipulatorswith 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 octahedralmanipulator 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 flaggedmanipulator. 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.
This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile.
Wire-based tracking devices are an affordable alternative to costly tracking devices. They consist of a fixed base and a platform, attached to the moving object, connected by six wires whose tension is maintained along the tracked trajectory. One important shortcoming of these devices is that they are forced to operate in reduced workspaces so as to avoid singular configurations. Singularities can be eliminated by adding more wires, but this causes more wire interferences, and a higher force exerted on the moving object by the measuring device itself. This paper shows how, by introducing a rotating base, the number of wires can be reduced to three, and singularities can be avoided by using an active sensing strategy. This also permits reducing wire interference problems and the pulling force exerted by the device.
This paper presents a relational positioning methodology that allows to restrict totally or partially the movements of an object by specifying its allowed positions in terms of a set of intuitive geometric constraints. In order to derive these positions, a geometric constraint solver must be used. To this end, positioning mobile with respect to fixed (PMF), a geometric constraint solver for the relational positioning of rigid objects in free space is introduced. The solver exploits the fact that, in a set of geometric constraints, the rotational component can often be separated from the translational one and solved independently. PMF may be used as an interface for specifying offline-programmed robot tasks, as well as for assisting the execution of teleoperated tasks requiring constrained movements. Examples describing both the solver’s operation and typical applications are discussed.
The conditions for a parallel manipulator to be flagged can be simply expressed in terms of linear dependencies between the coordinates of its leg attachments, both on the base and on the platform. These dependencies permit to describe the manipulator singularities in terms of incidences between two flags (hence, the name ldquoflaggedrdquo). Although these linear dependencies might look, at first glance, too restrictive, in this paper, the family of flagged manipulators is shown to contain large subfamilies of six-legged and three-legged manipulators. The main interest of flagged parallel manipulators is that their singularity loci admit a well-behaved decomposition with a unique topology irrespective of the metrics of each particular design. In this paper, this topology is formally derived and all the cells, in the configuration space of the platform, of dimension 6 (nonsingular) and dimension 5 (singular), together with their adjacencies, are worked out in detail.
The uncertainty of the odometry position estimate for a given vehicle can be obtained from the definition of the covariance matrix by using its kinematic model as well as its sensory system data. This communication item extends a previous work in  by giving the appropriate guidelines so as to compute the cross-covariance terms between the previous position estimate and the actual increments of position. This is necessary in general because the orientation errors on the robot’s previous position will affect the calculation of the actual increments of position.
Some in-parallel robots, such as the 3-2-1 and the 3/2 manipulators, have attracted attention because their forward kinematics can be solved by three consecutive trilaterations. In this paper, we identify a class of these robots, which we call flagged manipulators, whose singularity loci admit a well-behaved decomposition, i.e., a stratification, derived from that of the flag manifold. Two remarkable properties must be highlighted. First, the decomposition has the same topology for all members in the class, irrespective of the metric details of each particular robot instance. Thus, we provide explicitly all the singular strata and their connectivity, which apply to all flagged manipulators without any tailoring. Second, the strata can be easily characterized geometrically, because it is possible to assign local coordinates to each stratum (in the configuration space of the manipulator) that correspond to uncoupled rotations and/or translations in the workspace.
This paper deals with the problem of estimating the pose of a moving rigid body by measuring the length of six wires attached to it. Since wires can be seen as extensible legs, this problem is equivalent to that of solving the forward kinematics of a six-degree-of-freedom parallel manipulator. Among all possible locations for the attachments on the moving object, the "3-2-1" configuration is shown to exhibit a large number of favorable properties. The performance analysis of this particular configuration is addressed by finding analytic expressions for the estimated pose covariance matrix and the expected value of the pose estimation error, or bias error, which has been omitted in the previous analysis of wire-based tracking devices. This analysis takes advantage of a formulation for trilateration based on Cayley-Menger determinants, which is mathematically more tractable compared to previous ones, because all terms involved are determinants with geometric meaning. This accommodates a more thorough investigation of the properties of the device.
Given some geometric elements such as points and lines in R/sup 3/, subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in robotics (such as the position analysis of serial and parallel manipulators) and CAD/CAM (such as the interactive placement of objects) can be formulated in this way. The strategy herein proposed consists of looking for some of the a priori unknown distances, whose derivation permits solving the problem rather trivially. Finding these distances relies on a branch-and-prune technique, which iteratively eliminates from the space of distances entire regions which cannot contain any solution. This elimination is accomplished by applying redundant necessary conditions derived from the theory of distance geometry. The experimental results qualify this approach as a promising one.
Locating a robot from its distances, or range measurements, to three other known points or stations is a common operation, known as trilateration. This problem has been traditionally solved either by algebraic or numerical methods. An approach that avoids the direct algebrization of the problem is proposed here. Using constructive geometric arguments, a coordinate-free formula containing a small number of Cayley-Menger determinants is derived. This formulation accommodates a more thorough investigation of the effects caused by all possible sources of error, including round-off errors, for the first time in this context. New formulas for the variance and bias of the unknown robot location estimation, due to station location and range measurements errors, are derived and analyzed. They are proved to be more tractable compared with previous ones, because all their terms have geometric meaning, allowing a simple analysis of their asymptotic behavior near singularities.
The authors treat two different problems in the analysis of assemblies, and algorithms are described for each. The first problem is the selection of consistent sets of part feature relationships, and it corresponds to a search over possible configurations of parts that are consistent with feature set mappings. The second problem is the evaluation of the kinematic consistency of an assembly that has been defined by consistent feature sets. These two problems are linked together as two of the steps required in a search for all correct assembly configurations of a given set of parts. Several of the other necessary steps related to part interference, path feasibility, and workcell device kinematics are referred to but not analyzed. The proposed search algorithm is based on a constraint posting strategy, i.e. rather than generating and testing all specific alternatives, chunks of the search space are progressively removed from consideration by constraints that rule them out until one satisfactory alternative is found.
When a set of constraints is imposed on the degrees of freedom between several rigid bodies, finding the configuration or configurations that satisfy all these constraints is a matter of special interest. The problem is not new and has been discussed, not only in kinematics, but also more recently in the design of object-level robot programming languages. In this last domain, several languages have been developed, from different points of view, that are able to partially solve the problem. A more general method is derived than those previously proposed that were based on the symbolic manipulation of chains of matrix products, using the theory of continuous groups.