This paper presents amultisine approach for trajectory optimization based on information gain, with distance and orientation sensing to knownbeacons. It addresses the problem of active sensing, i.e. the selection of a robot motion or sequence of motions, which make the robot arrive in its desired goal configuration (position and orientation) with maximum accuracy, given the available sensor information. The optimal trajectory is parameterized as a linear combination of sinusoidal functions. Anappropriate optimality criterion is selected which takes into account various requirements (such as maximum accuracy and minimum time). Several constraints can be formulated, e.g. with respect to collision avoidance. The optimal trajectory is then determined by numerical optimization techniques. The approach is applicable to both nonholonomic and holonomic robots. Its effectiveness is illustrated here for a nonholonomic wheeled mobile robot (WMR) in an environment with and without obstacles.