Swarms of Non-holonomic Unicycle Agents with Model Uncertainty

Abstract

In this chapter, we consider a swarm composed of N agents whose dynamics have velocity constraints and evolve based on the equations

$$ \begin{array}{rcl} \dot{p}_{xi} & = & v_i\cos(\theta_i), \\ \dot{p}_{yi} & = & v_i\sin(\theta_i), \\ \dot{\theta}_i & = & w_i, \\ \dot{v}_i & = & \frac{1}{m_i}\left[u_{i1}+f_{v_i}\right], \\ \dot{w}_i & = & \frac{1}{I_i}\left[u_{i2}+f_{w_i}\right], \end{array} \label{eqn:unicycle_dynamics} $$

where $x_i(t)=[p_{xi}(t), p_{yi}(t)]^{\top}$ denotes the position of agent i at time instant t in cartesian coordinates, θ _i is the steering angle, v _i is the linear speed, and w _i is the angular speed of agent i. The quantities m _i and I _i are positive constants and represent the mass and the moment of inertia of agent i, respectively. The control inputs for agent i are the force input u_i1 = F _i and the torque input u_i2 = τ _i .