Robotics and Autonomous Systems 43 (2003) 231–243 A multisine approach for trajectory optimization based on information gain L. Mihaylova ∗ , J. De Schutter, H. Bruyninckx Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation, Katholieke Universiteit Leuven, Celestijnenlaan 300B, B-3001 Heverlee, Belgium Received 1 July 2002; received in revised form 28 January 2003 Communicated by F.C.A. Groen Abstract This paper presents a multisine approach for trajectory optimization based on information gain, with distance and orientation sensing to known beacons. 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 avail- able sensor information. The optimal trajectory is parameterized as a linear combination of sinusoidal functions. An appropriate 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. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Active sensing; Mobile robots; Uncertainty; Trajectory generation; Information gain 1. Motivation Many applications in mobile robotics have sophisti- cated motion requirements. A successful task comple- tion is often related to reaching quite accurately a goal while processing noisy sensor data under uncertain- ties. This refers to active sensing, the main question of which is: “What motion should the robot execute in order to gain (the most accurate) information about its environment?”. Active sensing is a challenging topic ∗ Corresponding author. Present address: Department of Elec- trical Energy, Systems and Automation, SYSTeMs Group, Uni- versiteit Gent, Technologiepark—Zwijnaarde 914, B-9052 Gent, Belgium. Fax: +32-16-32-2987. E-mail address: lyudmila.mihaylova@mech.kuleuven.ac.be (L. Mihaylova). for different reasons. The solution depends on the optimality criterion. This should be such that maxi- mum information is extracted from the sensor data. At the same time computationally efficient sensor data processing is needed for the on-line execution of the generated motions. Obstacle avoidance adds an another level of difficulty [20]. Uncertainty (e.g. in the model and sensor data) calls for stochastic estima- tion and control techniques. The nonlinear character of the problem adds further difficulty to this. Finally, for nonholonomic systems nonholonomic constraints have to be taken into account, so that the generated path from the admissible configuration space corre- sponds to a feasible trajectory [22,34]. This paper introduces an approach for trajectory op- timization based on information gain. A mobile robot is moving in the Cartesian plane starting from an initial 0921-8890/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-8890(03)00036-8