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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