Game theoretic controller synthesis for multi-robot motion planning Part I : Trajectory based algorithms

We consider a class of multi-robot motion planning problems where each robot is associated with multiple objectives and decoupled task specifications. The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game. The following properties are proven: (i) the algorithm asymptotically converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the price of stability equals one; (iii) for the worst case, the computational complexity and communication cost are linear in the robot number

THE IMPACT OF RECLAMATION ON ACCEPTABLE STRIP MINING ROYALTY PAYMENTS

Resource /Energy Economics and Policy,

Philosophy, mathematics and education

From Aristotle up to the Baroque knowledge was considered as essentially determined by its object. Since Kant and his so-called Copernican Revolution of Epistemology the epistemic subject and the method and means of its activities become equally, or even more important. Mathematics is, first of all, an activity, which has increasingly liberated itself from metaphysical and ontological agendas. As a consequence, the sense of mathematical symbolizations acquired partial independence from reference. The theories of modern science are schemes of interpretation of objective and socio-historical reality, rather than images of it. To observe the dynamics of the complementarity of sense and reference of symbolic representations becomes an important way of all knowledge related research. Perhaps more than any other practice, mathematical practice requires a complementarist approach, if its dynamics and meaning are to be properly understood

Bidirectional Sampling Based Search Without Two Point Boundary Value Solution

Bidirectional motion planning approaches decrease planning time, on average, compared to their unidirectional counterparts. In single-query feasible motion planning, using bidirectional search to find a continuous motion plan requires an edge connection between the forward and reverse search trees. Such a tree-tree connection requires solving a two-point Boundary Value Problem (BVP). However, a two-point BVP solution can be difficult or impossible to calculate for many systems. We present a novel bidirectional search strategy that does not require solving the two-point BVP. Instead of connecting the forward and reverse trees directly, the reverse tree's cost information is used as a guiding heuristic for the forward search. This enables the forward search to quickly converge to a feasible solution without solving the two-point BVP. We propose two new algorithms (GBRRT and GABRRT) that use this strategy and run multiple software simulations using multiple dynamical systems and real-world hardware experiments to show that our algorithms perform on-par or better than existing state-of-the-art methods in quickly finding an initial feasible solution.Comment: Journal version (Video: https://youtu.be/Rumg66UHfyQ