Robot audition refers to a range of hearing capabilities which help robots explore and understand their environment. Among them, sound source localization is the problem of estimating the location of a sound source given measurements of its angle of arrival with respect to a microphone array mounted on the robot. In addition, robot motion can help quickly solve the front-back ambiguity existing in a linear microphone array. In this article, we focus on the problem of exploiting robot motion to improve the estimation of the location of an intermittent and possibly moving source in a noisy and reverberant environment. We first propose a robust extended mixture Kalman filtering framework for jointly estimating the source location and its activity over time. Building on this framework, we then propose a long-term robot motion planning algorithm based on Monte Carlo tree search to find an optimal robot trajectory according to two alternative criteria: the Shannon entropy or the standard deviation of the estimated belief on the source location. These criteria are integrated over time using a discount factor. Experimental results show the robustness of the proposed estimation framework to false angle of arrival measurements within ±20◦ and 10% false source activity detection rate. The proposed robot motion planning technique achieves an average localization error 48.7% smaller than a one-step-ahead method. In addition, we compare the correlation between the estimation error and the two criteria, and investigate the effect of the discount factor on the performance of the proposed motion planning algorithm.