A path planning approach of 3D manipulators using zenithal gnomic projection and polar piecewise interpolation.

In this paper, the mathematical modeling and trajectory planning of a 3D rotating manipulator composed of a rotating-prismatic joint and multiple rigid links is considered. Possible trajectories of the end effector of the manipulator—following a sequence of 3D target points under the action of 2 external driving torques and an axial force—are modeled using zenithal gnomic projections and polar piecewise interpolants expressed as polynomial Hermite-type functions. Because of the geometry of the manipulator, the time-dependent generalized coordinates are associated with the spherical coordinates named the radial distance related to the manipulator length, and the polar and azimuthal angles describing the left and right and, respectively, up and down motion of the manipulator. The polar trajectories (left and right motion) of the end effector are generated using a inverse geometric transformation applied to the polar piecewise interpolants that approximate the gnomic projective trajectory of the 3D via-points. The gnomic via-points—located on a projective plane situated on the northern hemisphere—are seen from the manipulator base location, which represents the center of rotation of the extensible manipulator. The related azimuthal trajectory (up and down motion) is generated by polar piecewise interpolants on the azimuthal angles. Smoothness of the polygonal trajectory is obtained through the use of piecewise interpolants with continuous derivatives, while the kinematics and dynamics implementation of the model is well suited to computer implementation (easy calculation of kinematics variables) and simulation. To verify the approach and validate the model, a numerical example—implemented in Matlab—is presented, and the results are discussed

Environmental Modeling and Exposure Assessment of Sediment-Associated Pyrethroids in an Agricultural Watershed

Synthetic pyrethroid insecticides have generated public concerns due to their increasing use and potential effects on aquatic ecosystems. A modeling system was developed in this study for simulating the transport processes and associated sediment toxicity of pyrethroids at coupled field/watershed scales. The model was tested in the Orestimba Creek watershed, an agriculturally intensive area in California' Central Valley. Model predictions were satisfactory when compared with measured suspended solid concentration (R2 = 0.536), pyrethroid toxic unit (0.576), and cumulative mortality of Hyalella azteca (0.570). The results indicated that sediment toxicity in the study area was strongly related to the concentration of pyrethroids in bed sediment. Bifenthrin was identified as the dominant contributor to the sediment toxicity in recent years, accounting for 50–85% of predicted toxicity units. In addition, more than 90% of the variation on the annual maximum toxic unit of pyrethroids was attributed to precipitation and prior application of bifenthrin in the late irrigation season. As one of the first studies simulating the dynamics and spatial variability of pyrethroids in fields and instreams, the modeling results provided useful information on new policies to be considered with respect to pyrethroid regulation. This study suggested two potential measures to efficiently reduce sediment toxicity by pyrethroids in the study area: [1] limiting bifenthrin use immediately before rainfall season; and [2] implementing conservation practices to retain soil on cropland

Use-Exposure Relationships of Pesticides for Aquatic Risk Assessment

Field-scale environmental models have been widely used in aquatic exposure assessments of pesticides. Those models usually require a large set of input parameters and separate simulations for each pesticide in evaluation. In this study, a simple use-exposure relationship is developed based on regression analysis of stochastic simulation results generated from the Pesticide Root-Zone Model (PRZM). The developed mathematical relationship estimates edge-of-field peak concentrations of pesticides from aerobic soil metabolism half-life (AERO), organic carbon-normalized soil sorption coefficient (KOC), and application rate (RATE). In a case study of California crop scenarios, the relationships explained 90–95% of the variances in the peak concentrations of dissolved pesticides as predicted by PRZM simulations for a 30-year period. KOC was identified as the governing parameter in determining the relative magnitudes of pesticide exposures in a given crop scenario. The results of model application also indicated that the effects of chemical fate processes such as partitioning and degradation on pesticide exposure were similar among crop scenarios, while the cross-scenario variations were mainly associated with the landscape characteristics, such as organic carbon contents and curve numbers. With a minimum set of input data, the use-exposure relationships proposed in this study could be used in screening procedures for potential water quality impacts from the off-site movement of pesticides