1,339 research outputs found
Generic Singularities of Robot Manipulators
The singularities of the differential kinematic map, i.e. of the manipulator Jacobian, are considered. The authors first examine the notion of a generic kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator. For three-joint robots, an equivalent condition for genericity using determinants is derived. The condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators, i.e. manipulators that an be separated into a three-joint translating part and a three-joint orienting part. The results are illustrated by analyzing the singularities of two classes of three-joint positioning robots
Genericity and Singularities of Robot Manipulators
The kinematic singularities of robot manipulators are studied from the point of view of the theory of singularities. The notion of a generic\u27\u27 kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator, is examined. For three-joint robots, an equivalent algebraic condition for genericity using the Jacobian determinants is derived. This condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. Orientation and translation singularities of manipulators are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation singularities of the eight possible topologies of three-joint robots are studied and the conditions on the link parameters for nongenericity are determined
Workspace and Singularity analysis of a Delta like family robot
Workspace and joint space analysis are essential steps in describing the task
and designing the control loop of the robot, respectively. This paper presents
the descriptive analysis of a family of delta-like parallel robots by using
algebraic tools to induce an estimation about the complexity in representing
the singularities in the workspace and the joint space. A Gr{\"o}bner based
elimination is used to compute the singularities of the manipulator and a
Cylindrical Algebraic Decomposition algorithm is used to study the workspace
and the joint space. From these algebraic objects, we propose some certified
three dimensional plotting describing the the shape of workspace and of the
joint space which will help the engineers or researchers to decide the most
suited configuration of the manipulator they should use for a given task. Also,
the different parameters associated with the complexity of the serial and
parallel singularities are tabulated, which further enhance the selection of
the different configuration of the manipulator by comparing the complexity of
the singularity equations.Comment: 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun
2015, Poitiers, France. 201
An algebraic method to check the singularity-free paths for parallel robots
Trajectory planning is a critical step while programming the parallel
manipulators in a robotic cell. The main problem arises when there exists a
singular configuration between the two poses of the end-effectors while
discretizing the path with a classical approach. This paper presents an
algebraic method to check the feasibility of any given trajectories in the
workspace. The solutions of the polynomial equations associated with the
tra-jectories are projected in the joint space using Gr{\"o}bner based
elimination methods and the remaining equations are expressed in a parametric
form where the articular variables are functions of time t unlike any numerical
or discretization method. These formal computations allow to write the Jacobian
of the manip-ulator as a function of time and to check if its determinant can
vanish between two poses. Another benefit of this approach is to use a largest
workspace with a more complex shape than a cube, cylinder or sphere. For the
Orthoglide, a three degrees of freedom parallel robot, three different
trajectories are used to illustrate this method.Comment: Appears in International Design Engineering Technical Conferences &
Computers and Information in Engineering Conference , Aug 2015, Boston,
United States. 201
Uniqueness domains and non singular assembly mode changing trajectories
Parallel robots admit generally several solutions to the direct kinematics
problem. The aspects are associated with the maximal singularity free domains
without any singular configurations. Inside these regions, some trajectories
are possible between two solutions of the direct kinematic problem without
meeting any type of singularity: non-singular assembly mode trajectories. An
established condition for such trajectories is to have cusp points inside the
joint space that must be encircled. This paper presents an approach based on
the notion of uniqueness domains to explain this behaviour
Fast Manipulability Maximization Using Continuous-Time Trajectory Optimization
A significant challenge in manipulation motion planning is to ensure agility
in the face of unpredictable changes during task execution. This requires the
identification and possible modification of suitable joint-space trajectories,
since the joint velocities required to achieve a specific endeffector motion
vary with manipulator configuration. For a given manipulator configuration, the
joint space-to-task space velocity mapping is characterized by a quantity known
as the manipulability index. In contrast to previous control-based approaches,
we examine the maximization of manipulability during planning as a way of
achieving adaptable and safe joint space-to-task space motion mappings in
various scenarios. By representing the manipulator trajectory as a
continuous-time Gaussian process (GP), we are able to leverage recent advances
in trajectory optimization to maximize the manipulability index during
trajectory generation. Moreover, the sparsity of our chosen representation
reduces the typically large computational cost associated with maximizing
manipulability when additional constraints exist. Results from simulation
studies and experiments with a real manipulator demonstrate increases in
manipulability, while maintaining smooth trajectories with more dexterous (and
therefore more agile) arm configurations.Comment: In Proceedings of the IEEE International Conference on Intelligent
Robots and Systems (IROS'19), Macau, China, Nov. 4-8, 201
- …