Navigation tasks often cannot be defined in terms of a target, either because global position information is unavailable or unreliable or because target location is not explicitly known a priori. This task is then often defined indirectly as a source seeking problem in which the autonomous agent navigates so as to minimize the convex potential induced by a source while avoiding obstacles. This work addresses this problem when only scalar measurements of the potential are available, i.e., without gradient information. To do so, it construct an artificial potential over which an exact gradient dynamics would generate a collision-free trajectory to the target in a world with convex obstacles. Then, leveraging extremum seeking control loops, it minimizes this artificial potential to navigate smoothly to the source location. We prove that the proposed solution not only finds the source, but does so while avoiding any obstacle. Numerical results with velocity-actuated particles, simulations with an omni-directional robot in ROS+Gazebo, and a robot-in-the-loop experiment are used to illustrate the performance of this approach.
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