The performance of a mobile sensor network is measured by its ability to survey regions of interest efficiently and accurately with limited resources. Approaches for sampling trajectory optimization allow for adaptive algorithms that offer significant improvements in mapping error when compared with non-adaptive approaches.This thesis proposes an algorithm for generating adaptive sampling trajectories for a collaborative multi-agent team with heterogeneous mobility and sensing capabilities. Each agent, modeled as a differential thrust vehicle, contributes to the team's estimate of an unknown attribute in a region of interest by traversing the space while in communication with a centralized planner. The spatial distribution of the attribute is modeled as a stationary, isotropic Gaussian random field. Noisy local measurements of the attribute are synthesized into a global estimate of the underlying field using a Gaussian process regression technique known as kriging. A modified kriging method is proposed to accommodate the potential heterogeneity of measurement errors while improving computation time. A Voronoi-based algorithm is proposed which periodically partitions the sampling space to identify high-value sampling locations. Each agent's path is constructed using waypoints which compose an analogous mechanical system where virtual springs and masses connect sequential waypoints and mass centroids of Voronoi cells. By modeling each waypoint as a point mass within this spring-mass-damper system, an equilibrium position can be identified using an iterative process by which the system constraints are satisfied through the simulation of a virtual agent through the proposed waypoint set.Numerical simulations compare the proposed strategy with non-adaptive traversal of a Gaussian random field to validate the effectiveness of the proposed solution. The simulation results show a marked improvement when compared with the non-adaptive sampling methods in scalar fields with sufficient variability in space. The approach is also demonstrated through field experiments conducted on Lake Norman, NC using two custom designed autonomous surface vessel (ASV) mobile sensing platforms to observe bathymetric data. The mechanical, electrical and software design of the ASVs developed for this work is discussed.