Obstacle avoidance in formation using navigation-like functions and constraint based programming

In this paper, we combine navigation function-like potential fields and constraint based programming to achieve obstacle avoidance in formation. Constraint based programming was developed in robotic manipulation as a technique to take several constraints into account when controlling redundant manipulators. The approach has also been generalized, and applied to other control systems such as dual arm manipulators and unmanned aerial vehicles. Navigation functions are an elegant way to design controllers with provable properties for navigation problems. By combining these tools, we take advantage of the redundancy inherent in a multi-agent control problem and are able to concurrently address features such as formation maintenance and goal convergence, even in the presence of moving obstacles. We show how the user can decide a priority ordering of the objectives, as well as a clear way of seeing what objectives are currently addressed and what are postponed. We also analyze the theoretical properties of the proposed controller. Finally, we use a set of simulations to illustrate the approach.