Iterative optimisation in dynamic environments via local pursuit

We discuss an iterative optimal control approach in which a multi-agent group of control systems discovers locally optimal trajectories in environments with time-varying terrain geometry and moving, deforming obstacles. Works in literature have addressed only special cases of this problem with time-invariant terrain geometry. One such bio-inspired optimal control approach, applicable in static environments, is 'local pursuit', a method that iteratively solves partially-constrained final state problems by having agents follow one another, each agent moving optimally towards its predecessor. We show that if, instead, agents evolve in their own time-delayed 'copy' of the environment and act based on the most recent time history of their predecessors local neighbourhoods, then the original method can be extended to the dynamic environments described above. Furthermore, we discuss the computational complexity of our approach and demonstrate its effectiveness and computational advantages in a series of simulations.