The harmonic potential field of an incompressible nonviscous fluid governed by the Laplace’s Equation has shown its potential for being beneficial to autonomous unmanned vehicles to generate smooth, natural-looking, and predictable paths for obstacle avoidance. The streamlines generated by the boundary value problem of the Laplace’s Equation have explicit, easily computable, or analytic vector fields as the path tangent or robot heading specification without the waypoints and higher order path characteristics. We implemented an obstacle avoidance approach with a focus on curvature constraint for a non-holonomic mobile robot regarded as a particle using curvature-constrained streamlines and streamline changing via pure pursuit. First, we use the potential flow field around a circle to derive three primitive curvature-constrained paths to avoid single obstacles. Furthermore, the pure pursuit controller is implemented to achieve a smooth transition between the streamline paths in the environment with multiple obstacles. In addition to comparative simulations, a proof of concept experiment implemented on a two-wheel driving mobile robot with range sensors validates the practical usefulness of the integrated system that is able to navigate smoothly and safely among multiple cylinder obstacles. The computational requirement of the obstacle avoidance system takes advantage of an a priori selection of fast computing primitive streamline paths, thus, making the system able to generate online a feasible path with a lower maximum curvature that does not violate the curvature constraint.

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The time-optimal control problem (TOCP) has faced new practical challenges, such as those from the deployment of agile autonomous vehicles in diverse uncertain operating conditions without accurate system calibration. In this study to meet a need to generate feasible speed profiles in the face of uncertainty, we exploit and implement probabilistic inference for learning control (PILCO), an existing sample-efficient model-based reinforcement learning (MBRL) framework for policy search, to a case study of TOCP for a vehicle that was modeled as a constant input-constrained double integrator with uncertain inertia subject to uncertain viscous friction. Our approach integrates learning, planning, and control to construct a generalizable approach that requires minimal assumptions (especially regarding external disturbances and the parametric dynamics model of the system) for solving TOCP approximately as the perturbed solutions close to time-optimality. Within PILCO, a Gaussian Radial basis functions is implemented to generate control-constrained rest-to-rest near time-optimal vehicle motion on a linear track from scratch with data-efficiency in a direct way. We briefly introduce the importance of the applications of PILCO and discuss the learning results that PILCO would actually converge to the analytical solution in this TOCP. Furthermore, we execute a simulation and a sim2real experiment to validate the suitability of PILCO for TOCP by comparing with the analytical solution.

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