Attractor dynamics generates robot formation: from theory to implementation

We show how non-linear attractor dynamics can be used to implement robot formations in unknown environments. The desired formation geometry is given through a matrix where the parameters in each line (its leader, desired distance and relative orientation to the leader) define the desired pose of a robot in the formation. The parameter values are then used to shape the vector fields of the dynamical systems that generate values for the control variables (i.e. heading direction and path velocity). Then these dynamical systems are tuned such that the control variables are always very close to one of the resultant attractors. The advantage is that the systems are more robust against perturbations because the behavior is generated as a time series of asymptotically stable states. Experimental results (with three Khepera robots) demonstrate the ability of the team to create and stabilize the formation, as well as avoiding obstacles. Flexibility is achieved in that as the senses world changes, the systems may change their planning solutions continuously but also discontinuously (tuning the formation versus split to avoid obstacle).