This paper addresses the problem of minimizing the uncertainty through motion planning in a globally exponentially stable sensor-based simultaneous localization and mapping algorithm, with the objective of performing active exploitation. This is done by designing an optimization problem that weighs the final uncertainty, the overall uncertainty in the horizon considered, and the cost of the control. Using the Pontryagin minimum principle and building on the derivation of the Kalman filter by Athans and Tse as well as on Hussein's extension for motion planning, the optimization problem is transformed into a two-point boundary value problem that encodes necessary conditions for the input that minimizes the uncertainty. A strategy is proposed to solve this problem numerically, and particular examples are analysed. Following the shortcomings identified in this procedure, the original optimization problem is modified assuming that the input velocities are piecewise constant functions. A direct approach is used to solve this new optimization problem, allowing the in-depth analysis of more realistic scenarios.