In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional ...
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In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, A(n - 1,0) = sl(1 vertical bar n) can be constructed by adding a "gray" node to the Dynkin diagram of A(n-1) = sl(n), corresponding to an odd null root. The Cartan superalgebras constitute a different class, where the simplest example is W(n), the derivation algebra of the Grassmann algebra on n generators. Here we present a novel construction of W(n), from the same Dynkin diagram as A(n - 1,0), but with additional generators and relations.
Ad Hoc networks are characterized as fast time-varying. Thus, fast distributed algorithm to implement self-management is indispensable, especially for QoS support. In this paper, we propose rate control with QoS suppo...
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Ad Hoc networks are characterized as fast time-varying. Thus, fast distributed algorithm to implement self-management is indispensable, especially for QoS support. In this paper, we propose rate control with QoS support in Ad Hoc networks based on primal-dual interior-point method. We apply Gaussian belief propagation algorithm to compute the Newton step. For implementing distributed computation in practical network, we design the mapping rules between GaBP-mapping network and the practical networks. Finally, the simulation results show that the proposed algorithm has favorable performance, including fast convergence, robustness and scalability.
In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven te...
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ISBN:
(纸本)9781509047192
In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force/torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit.
A dynamic model to study the vibration characteristics of a submarine propeller-shaft-hull system is developed using the FRF-based substructuring method (FBSM). The propeller-shaft system and the hull is firstly model...
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