This paper studies a core problem in multi-objective mission planning for robots governed by differential constraints. The problem considered is the following. A car-like robot computes a plan to move from a start configuration to a goal region. The robot is equipped with a sensor that can alert it if an anomaly appears within some range while the robot is moving. In that case, the robot tries to deviate from its computed path and gather more information about the target without incurring considerable delays in fulfilling its primary mission, which is to move to its final destination. This problem is important in, e.g., surveillance, where inspection of possible threats needs to be balanced with completing a nominal route. The paper presents a simple and intuitive framework to study the trade-offs present in the above problem. Our work utilizes a state-of-the-art sampling-based planner, which employs both a high-level discrete guide and low-level planning. We show that modifications to the distance function used by the planner and to the weights that the planner employs to compute the high-level guide can help the robot react online to new secondary objectives that were unknown at the outset of the mission. The modifications are computed using information obtained from a conventional camera model. We find that for small percentage increases in path length, the robot can achieve significant gains in information about an unexpected target.