Trajectory planning for multiple robots in bearing-only target localisation

This paper provides a solution to the optimal trajectory planning problem in target localisation for multiple heterogeneous robots with bearing-only sensors. The objective here is to find robot trajectories that maximise the accuracy of the locations of the targets at a prescribed terminal time. The trajectory planning is formulated as an optimal control problem for a nonlinear system with a gradually identified model and then solved using nonlinear model predictive control (MPC). The solution to the MPC optimisation problem is computed through exhaustive expansion tree search (EETS) plus sequential quadratic programming (SQP). Simulations were conducted using the proposed methods. Results show that EETS alone performs considerably faster than EETS+SQP with only minor differences in information gain, and that a centralised approach outperforms a decentralised one in terms of information gain. We show that a centralised EETS provides a near optimal solution. We also demonstrate the significance of using a matrix to represent the information gathered.