Synthesis of spatial RPRP closed linkages for a given screw system

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end-effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negative mobility. These problems can be avoided for some overconstrained but movable linkages if the finite-screw system associated with the motion of the linkage is known. The finite-screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite task positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.Postprint (author’s final draft

Grasping unknown objects in clutter by superquadric representation

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, a quick and efficient method is presented for grasping unknown objects in clutter. The grasping method relies on real-time superquadric (SQ) representation of partial view objects and incomplete object modelling, well suited for unknown symmetric objects in cluttered scenarios which is followed by optimized antipodal grasping. The incomplete object models are processed through a mirroring algorithm that assumes symmetry to first create an approximate complete model and then fit for SQ representation. The grasping algorithm is designed for maximum force balance and stability, taking advantage of the quick retrieval of dimension and surface curvature information from the SQ parameters. The pose of the SQs with respect to the direction of gravity is calculated and used together with the parameters of the SQs and specification of the gripper, to select the best direction of approach and contact points. The SQ fitting method has been tested on custom datasets containing objects in isolation as well as in clutter. The grasping algorithm is evaluated on a PR2 robot and real time results are presented. Initial results indicate that though the method is based on simplistic shape information, it outperforms other learning based grasping algorithms that also work in clutter in terms of time-efficiency and accuracy.Peer ReviewedPostprint (author's final draft

Singularity-free computation of quaternions from rotation matrices in E4 and E3

A real orthogonal matrix representing a rotation in E4 can be decomposed into the commutative product of a left-isoclinic and a right-isoclinic rotation matrix. The double quaternion representation of rotations in E4 follows directly from this decomposition. In this paper, it is shown how this decomposition can be performed without divisions. This avoids the common numerical issues attributed to the computation of quaternions from rotation matrices. The map from the 4×4 rotation matrices to the set of double unit quaternions is a 2-to-1 covering map. Thus, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clari¿ed. When particularized to three dimensions, it is shown how the resulting formulation outperforms, from the numerical point of view, the celebrated Shepperd’s method.Peer ReviewedPostprint (author's final draft

On Cayley's factorization with an application to the orthonormalization of noisy rotation matrices

The final publication is available at link.springer.comA real orthogonal matrix representing a rotation in four dimensions can be decomposed into the commutative product of a left- and a right-isoclinic rotation matrix. This operation, known as Cayley's factorization, directly provides the double quaternion representation of rotations in four dimensions. This factorization can be performed without divisions, thus avoiding the common numerical issues attributed to the computation of quaternions from rotation matrices. In this paper, it is shown how this result is particularly useful, when particularized to three dimensions, to re-orthonormalize a noisy rotation matrix by converting it to quaternion form and then obtaining back the corresponding proper rotation matrix. This re-orthonormalization method is commonly implemented using the Shepperd-Markley method, but the method derived here is shown to outperform it by returning results closer to those obtained using the Singular Value Decomposition which are known to be optimal in terms of the Frobenius norm.Peer ReviewedPostprint (author's final draft

Dimensional Synthesis of Wristed Binary Hands

The kinematic synthesis applied to tree topologies is a tool for the design of multi-fingered robotic hands, for a simultaneous task of all fingertips. Even though traditionally wrists and hands have been designed separately, the wrist usually being part of the robot manipulator arm, it makes sense to consider the wrist as a part of the hand, as many grasping and manipulation actions are a coordinated action of wrist and fingers. The manipulation capabilities of robotic hands mayalso beenhancedbyconsidering more than one splitting stage, as opposed to the single-palm traditional hand. In this work we present the dimensional synthesis for a family of multi-fingered hands, the binary hands, which have a 2R wrist and several splitting stages, each of them spanning two branches consisting f a revolute joint for each edge. For these topologies, it is proved that a three-position task can be defined for each fingertip, regardless of the number of fingers. One example is presented to show the possible design strategies and uses for this family of hands.Postprint (published version

Mixed Position and Twist Space Synthesis of 3R Chains

Mixed-position kinematic synthesis is used to not only reach a certain number of precision positions, but also impose certain instantaneous motion conditions at those positions. In the traditional approach, one end-effector twist is defined at each precision position in order to achieve better guidance of the end-effector along a desired trajectory. For one-degree-of-freedom linkages, that suffices to fully specify the trajectory locally. However, for systems with a higher number of degrees of freedom, such as robotic systems, it is possible to specify a complete higher-dimensional subspace of potential twists at particular positions. In this work, we focus on the 3R serial chain. We study the three-dimensional subspaces of twists that can be defined and set the mixed-position equations to synthesize the chain. The number and type of twist systems that a chain can generate depend on the topology of the chain; we find that the spatial 3R chain can generate seven different fully defined twist systems. Finally, examples of synthesis with several fully defined and partially defined twist spaces are presented. We show that it is possible to synthesize 3R chains for feasible subspaces of different types. This allows a complete definition of potential motions at particular positions, which could be used for the design of precise interaction with contact surfaces.Peer ReviewedPostprint (author's final draft

Bennet's Linkage and the Cylindroid

Bennett’s linkage is a spatial 4R closed chain that can move with one degree of freedom. The set of relative displacement screws that form the one-dimensional workspace of this device defines a ruled surface known as a cylindroid. The cylindroid is generally obtained as a result of a real linear combination of two screws. Thus, the workspace of Bennett’s linkage is directly related to a one-dimensional linear subspace of screws. In this paper, we examine in detail Bennett’s linkage and its associated cylindroid, and introduce a reference pyramid which provides a convenient way to relate the two. These results are fundamental to efficient techniques for solving the synthesis equations for spatial RR chains.Peer ReviewedPostprint (published version

Humanoid synthesis using clifford algebra

One of the challenges in the simulation of human motion, either applied to humanoid robots or avatars in virtual environments, is to design a kinematics structure and a set of joint trajectories that move a robot or avatar in a human-like manner. In this paper, a technique is introduced to create accurate humanlike motion with a simplified topology as a reference. Using an optical motion capture system, a finite number of key poses are captured from different subjects performing full body articulated movements. Motion is modeled using the Clifford algebra of dual quaternions and dimensional synthesis techniques are applied to generate the kinematic skeleton of a 3D avatar or robot. The synthesized kinematic skeleton provides location of joints and dimensions of the links forming the limbs, as well as the joint trajectories. Five serial chains constitute our approximation to the human skeleton. Revolute, universal and spherical joints are employed, although other topologies can be used in a similar fashion. Several real datasets are evaluated and results demonstrate that good accuracy can be obtained at interactive rates using the presented methodology. The results show that using simple serial chains in combination with dimensional synthesis suffices to generate the mechanical structure and trajectories of a humanoid robot or 3D avatar mimicking human motion.Postprint (author’s final draft

Design of non-anthropomorphic robotic hands for anthropomorphic tasks

In this paper, we explore the idea of designing non- anthropomorphic multi-fingered robotic hands for tasks tha t replicate the motion of the human hand. Taking as input data a finite set of rigid-body positions for the five fingertips, we de- velop a method to perform dimensional synthesis for a kinema tic chain with a tree structure, with five branches that share thr ee common joints. We state the forward kinematics equations of relative dis- placements for each serial chain expressed as dual quaterni ons, and solve for up to five chains simultaneously to reach a numbe r of positions along the hand trajectory. This is done using a h y- brid global numerical solver that integrates a genetic algo rithm and a Levenberg-Marquardt local optimizer. Although the number of candidate solutions in this problem is very high, the use of the genetic algorithm allows us to per form an exhaustive exploration of the solution space to obtain a s et of solutions. We can then choose some of the solutions based on t he specific task to perform. Note that these designs match the ta sk exactly while generally having a finger design radically dif ferent from that of the human hand.Peer ReviewedPostprint (author’s final draft

A Task-based Design Methodology for Robotic Exoskeletons

This study is aimed at developing a task-based methodology for the design of robotic exoskeletons. This is in contrast to prevailing research efforts, which attempt to mimic the human limb, where each human joint is given an exoskeleton counter-joint. Rather, we present an alternative systematic design approach for the design of exoskeletons that can follow the complex three-dimensional motions of the human body independent of anatomical measures and landmarks. With this approach, it is not necessary to know the geometry of the targeted limb but rather to have a description of its motion at the point of attachment.Peer ReviewedObjectius de Desenvolupament Sostenible::3 - Salut i BenestarPostprint (published version