This paper considers the optimal control problem of steering a Dubins vehicle with a decaying speed that depends linearly on the turn-rate to a terminal point and heading with maximum kinetic energy. Pontryagin’s minimum principle is applied and the extremals are identified as sequences of straight segments and spiral-shaped turns described by involutes of a circle. A method is proposed to exactly transcribe the optimal control problem into a series of finite dimensional optimizations. Each of these optimizations determines a locally optimal candidate path that reaches the terminal state. The lowest cost path among the candidate paths is then identified. The approach is demonstrated through several numerical examples.

This paper presents an algorithm for a team of heterogeneous mobile robots to estimate and adaptively sample a stationary, isotropic, Gaussian process. An estimation framework is proposed to assimilate measurements from robots with differing sensing capabilities (i.e., measurement noise variance). To improve computational efficiency of the Gaussian process regression, the survey area is divided into regions that each use a common semivariogram matrix constructed with a truncated measurement set determined by an adaptive selector. As the mission proceeds, a Voronoi-based algorithm periodically partitions a density function-representing time-varying sampling priority-to identify high-value sampling locations. The path for each robot is modeled as an mechanical system: a sequence of masses (waypoints) are interconnected by springs and dampers and pulled towards Voronoi cell centroids. At each path planning cycle the robots are iteratively simulated with heterogeneous dynamics (e.g., speed, turn radius) following their respective waypoint paths as stiffness/damping parameters are adjusted to satisfy mission time constraints. Numerical simulations show that the proposed approach reduces mapping error when compared to non-adaptive lawnmower coverage of a survey area. The algorithm is demonstrated experimentally using two cooperating autonomous surface vessels to map the bathymetry in a section of Lake Norman near Charlotte, NC.