11,651 research outputs found
A randomized kinodynamic planner for closed-chain robotic systems
Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin
A fast branch-and-prune algorithm for the position analysis of spherical mechanisms
The final publication is available at link.springer.comDifferent branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.Peer ReviewedPostprint (author's final draft
Self-Motions of General 3-RPR Planar Parallel Robots
This paper studies the kinematic geometry of general 3-RPR planar parallel
robots with actuated base joints. These robots, while largely overlooked, have
simple direct kinematics and large singularity-free workspace. Furthermore,
their kinematic geometry is the same as that of a newly developed parallel
robot with SCARA-type motions. Starting from the direct and inverse kinematic
model, the expressions for the singularity loci of 3-RPR planar parallel robots
are determined. Then, the global behaviour at all singularities is
geometrically described by studying the degeneracy of the direct kinematic
model. Special cases of self-motions are then examined and the degree of
freedom gained in such special configurations is kinematically interpreted.
Finally, a practical example is discussed and experimental validations
performed on an actual robot prototype are presented
Landau Singularities from the Amplituhedron
We propose a simple geometric algorithm for determining the complete set of
branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from
the amplituhedron, without resorting to any particular representation in terms
of local Feynman integrals. This represents a step towards translating
integrands directly into integrals. In particular, the algorithm provides
information about the symbol alphabets of general amplitudes. We illustrate the
algorithm applied to the one- and two-loop MHV amplitudes.Comment: 34 pages, 16 figures; v2: minor corrections and improvement
A Developmental Organization for Robot Behavior
This paper focuses on exploring how learning and development can be structured in synthetic (robot) systems. We present a developmental assembler for constructing reusable and temporally extended actions in a sequence. The discussion adopts the traditions
of dynamic pattern theory in which behavior
is an artifact of coupled dynamical systems
with a number of controllable degrees of freedom. In our model, the events that delineate
control decisions are derived from the pattern
of (dis)equilibria on a working subset of sensorimotor policies. We show how this architecture can be used to accomplish sequential
knowledge gathering and representation tasks
and provide examples of the kind of developmental milestones that this approach has
already produced in our lab
Port-Hamiltonian systems: an introductory survey
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models
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