One of the core functions in most Evolutionary Algorithms is mutation. In complex search spaces, which are common in Evolutionary Robotics, mutation is often used both for optimizing existing solutions, described as exploitation, and for spanning the search space, called exploration. This presents a difficult challenge for researchers as mutation parameters must be selected with care in order to balance the two, often contradictory, effects. Strategies that vary mutation during the search often try to estimate these effects in order to modify the mutation parameters. In this regard MAP-Elites, a Quality Diversity algorithm, presents an interesting opportunity. Because factors related to exploration and exploitation are readily available during the search, optimization based on these factors could be utilized to improve the search. In this paper we study how online adaptation of mutation rate, dynamic mutation, affects MAP-Elites in order to gain insight into how the search process is affected by the mutation rate. Our study compares fixed and dynamic mutation parameters for two different complex gait controllers. The results show that dynamic mutation combines favorably with MAP-Elites and that there is a strong relation between mutation parameters and exploration that can be utilized.