Abstract-In this paper we consider the problem of controlling multiple robots manipulating and transporting a payload in three dimensions via cables. We develop robot configurations that ensure static equilibrium of the payload at a desired pose while respecting constraints on the tension and provide analysis of payload stability for these configurations. We demonstrate our methods on a team of aerial robots via simulation and experimentation.

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We have investigated the effect of a solidifying crust on the dynamics and surface morphology of radial viscous-gravity currents. Liquid polyethylene glycol was admitted into the base of a tank filled with cold sucrose solution maintained at a temperature below the wax freezing point. As the radial current advanced away from the inlet, its surface solidified and deformed through a combination of folding and fracturing. For the warmest experiments, during which solidification did not occur, the radius of the current increased in proportion to the square root of time, as demonstrated both experimentally and theoretically for isothermal viscous fluids by Huppert (1982). When cooling was sufficiently rapid, solid crust formed and caused the spreading rate to decrease. A cooling model combining conduction in the wax with convection in the sucrose solution predicts the distance from the source at which the solid crust first appearedProgressively colder experiments revealed a sequence of surface morphologies which resembled features observed on cooling lava flows and lava lakes. Flows in which crust formed very slowly developed marginal levees which contained and channelled the main portion of the current. Colder flows with more rapid crust growth formed regularly spaced surface folds, multi-armed rift structures complete with shear offsets, and bulbous lobate forms similar to pillow lavas seen under the ocean. The same transitions between modes of surface deformation were also generated by keeping the ambient water temperature constant and decreasing the extrusion rate. This demonstration that surfaces can exhibit a well-defined sequence of morphologies which depend on the underlying flow conditions offers the prospect of more successful interpretation of natural lava flows.

Recent years have seen a number of challenges to social stability and order, ranging from terrorist attacks and natural disasters to epidemics such as AIDS and SARS. Such challenges have generated specific policy responses, such as enhanced security at transportation hubs and planned deployment of a global tsunami detection network. However, the range of challenges and the practical impossibility of adequately addressing each in turn argue for adoption of a more comprehensive systems perspective. This should be based on the principle of enhancing social and economic resiliency as well as meeting security and emergency response needs and, to the extent possible, developing and implementing dual-use technologies that offer societal benefits even if anticipated disasters never occur.

The results of recent laboratory experiments with wax extruded beneath relatively cold water may be extrapolated to predict the surface morphology of submarine lavas as a function of the extrusion rate and melt viscosity. The experiments with solidifying wax indicated that the surface morphology was controlled by a single parameter, the ratio of the time taken for the surface to solidify, and a time scale for lateral flow. For submarine basalts a solution of the cooling problem (which is dominated by conduction in the lava but convective heat transfer in the water) and estimates of lava viscosities place this parameter within the empirically determined “pillowing” regime over a wide range of extrusion rates. This result is consistent with the observation that pillow basalts are the most common products of submarine eruptions. Smoother surfaces corresponding to the various types of submarine sheet flows are predicted for sufficiently rapid extrusions of basaltic magma. Still higher eruption rates in regions of low topographic relief may produce submarine lava lakes. Minimum emplacement times can be calculated for submarine volcanic constructs of a single lava flow type.

Abstract-In this paper we consider the problem of controlling multiple robots manipulating and transporting a payload in three dimensions via cables. We develop robot configurations that ensure static equilibrium of the payload at a desired pose while respecting constraints on the tension and provide analysis of payload stability for these configurations. We demonstrate our methods on a team of aerial robots via simulation and experimentation.

We consider the planning and control of multiple aerial robots manipulating and transporting a payload in three dimensions via cables. Individual robot control laws and motion plans enable the control of the payload (position and orientation) along a desired trajectory. We address the fact that robot configurations may admit multiple payload equilibrium solutions by developing constraints for the robot configuration that guarantee the existence of a unique payload pose. Further, we formulate individual robot control laws that enforce these constraints and enable the design of non-trivial payload motion plans. Finally, we propose two quality measures for motion plan design that minimize individual robot motion and maximize payload stability along the trajectory. The methods proposed in the work are evaluated through simulation and experimentation with a team of three quadrotors.

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