Reactive exploration through following isolines in a potential field

Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey

“…Linear powered device (PD) controller fed by the current field value was proposed in ref. [17] for steering a unicycle-like vehicle along a level curve of a field given by a radial harmonic function, and a local convergence result was established for a vehicle with unlimited control range.…”

Curve Tracking Control for Autonomous Vehicles with Rigidly Mounted Range Sensors

“…A decentralized coordination algorithm for multiple vehicles to locate and track a dynamic perimeter is presented in [17]. The authors of [18] proposed a control law for following isolines in a potential field not relying on higher order characteristics of the field such as the gradient at a point or the curvature of the isolines. Conditions for nonlinear switched system to be asymptotically stable were presented in [19].…”

Cooperative surveillance of unknown environmental boundaries by multiple nonholonomic robots

“…These works are based, more or less, on heuristics and offer no rigorous and completed justification of the proposed control laws. Linear PD controller fed by only the current field value was presented in [23] for steering a Dubins car like vehicle along a level curve of a radial harmonic field, and a local convergence result was established with assuming an unlimited control range. A sliding mode control method for tracking environmental level sets without gradient estimation was offered in [24].…”

“…A sliding mode control method for tracking environmental level sets without gradient estimation was offered in [24]. At the same time, [23,24] were confined to the case where the sensor moves at a constant longitudinal speed and is controlled by the angular velocity. The results and recommendations of [23,24] do not extend on the case of a time-varying speed.…”