Constrained multi-agent ergodic area surveying control based on finite element approximation of the potential field

Abstract

Heat Equation Driven Area Coverage (HEDAC) is a state-of-the-art multi-agent ergodic motion control guided by a gradient of a potential field. A finite element method is hereby implemented to obtain a solution of Helmholtz partial di erential equation, which models the potential field for surveying motion control. This allows us to survey arbitrarily shaped domains and to include obstacles in an elegant and robust manner intrinsic to HEDAC's fundamental idea. For a simple kinematic motion, the obstacles and boundary avoidance constraints are successfully handled by directing the agent motion with the gradient of the potential. However, including additional constraints, such as the minimal clearance dsitance from stationary and moving obstacles and the minimal path curvature radius, requires further alternations of the control algorithm. We introduce a relatively simple yet robust approach for handling these constraints by formulating a straightforward optimization problem based on collision-free escapes route maneuvers. This approach provides a guaranteed collision avoidance mechanism, while being computationally inexpensive as a result of the optimization problem partitioning. The proposed motion control is evaluated in three realistic surveying scenarios simulations, showing the e ectiveness of the surveying and the robustness of the control algorithm. Furthermore, potential maneuvering di culties due to improperly defined surveying scenarios are highlighted and we provide guidelines on how to overpass them. The results are promising and indiacate real-world applicability of proposed constrained multi-agent motion control for autonomous surveying and potentially other HEDAC utilizations.

Multi-UAV trajectory planning for 3D visual inspection of complex structures

“…Improvement of the HEDAC algorithm for multi-agent surveying constrained motion control in irregular domains is proposed in [15]. The previous implementation considered rectangular domains due to using the finite difference method for solving a partial differential equation regulating the potential.…”

“…The smoothness of the Gaussian function allows better stability and smooth motion because the coverage is accumulated near the trajectory. The use of the Gaussian function in the HEDAC control is utilized and proven in numerical experiments in two-dimensional coverage motion control applications [12,14,15]. This instantaneous action can be defined as:…”

“…Several different approaches for boundary and inter-UAV collision avoidance were successfully utilized in twodimensional HEDAC applications [12,15]. When compared to the collision avoidance in two dimensions, the threedimensional case has more degrees of freedom hence the probability of random collisions between UAVs is greatly reduced but they do occur eventually if no collision avoidance procedure is implemented.…”