This paper describes a low computational direct approach for optimal motion planning and obstacle avoidance of Omni-directional mobile robots within velocity and acceleration constraints on the robot motion. The main purpose of this problem is the minimization of a quadratic cost function while limitation on velocity and acceleration of robot is considered and collision with any obstacle in the...

We assume a differential drive mobile robot: two unsteered coaxial wheels are independently actuated. Each wheel has bounded velocity, but no bound on torque or acceleration. Pontryagin’s Maximum Principle gives an elegant description of the extremal trajectories, which are a superset of the time optimal trajectories. Further analysis gives an enumeration of the time optimal trajectories, and m...

In many unmanned aerial vehicle (UAV) applications for surveillance and data collection, it is not possible to reach all requested locations due the given maximum flight time. Hence, must be prioritized problem of selecting most important modeled as an Orienteering Problem (OP). To fully exploit kinematic properties UAV in such scenarios, we combine OP with generation time-optimal trajectories ...

This paper applies Pontryagin’s Maximum Principle to the time optimal control of differential drive mobile robots with velocity bounds. The Maximum Principle gives necessary conditions for time optimality. Extremal trajectories are those which satisfy these conditions, and are thus a superset of the time optimal trajectories. This paper derives a compact geometrical structure for extremal traje...

This paper presents the time optimal trajectories for differential drive vehicles in the unobstructed plane. The wheel angular velocities are bounded, but may be discontinuous. The paper proves the existence of optimal controls, derives the structure of optimal trajectories, and develops an algorithm for producing a time optimal trajectory between any two configurations. Every nontrivial optima...

Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associa...