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A discrete time, optimal trajectory planning scheme for position trajectory generation of a vehicle is given here, considering the mission duration as a free variable. The vehicle is actuated in three rotational degrees of freedom and one translational degree of freedom. This model is applicable to vehicles that have a body-fixed thrust vector direction for translational motion control, including fixed-wing and rotorcraft unmanned aerial vehicles (UAVs), unmanned underwater vehicles (UUVs) and spacecraft. The lightweight scheme proposed here generates the trajectory in inertial coordinates, and is intended for real time, on-the-go applications. The unspecified terminal time can be considered as an additional design parameter. This is done by deriving the optimality conditions in a discrete time setting, which results in the discrete transversality condition. The trajectory starts from an initial position and reaches a desired final position in an unspecified final time that ensures the cost on state and control is optimized. The trajectory generated by this scheme can be considered as the desired trajectory for a tracking control scheme. Numerical simulation results validate the performance of this trajectory generation scheme used in conjunction with a nonlinear tracking control scheme. 

In this paper, finite-time attitude consensus control laws for multi-agent rigid body systems are presented using rotation matrices. The control objective is to stabilize the relative configurations in a finite convergence time. First, the control design is done on the kinematic level where the angular velocities are the control signals. Next, the design is conducted on the dynamic level in the framework of the tangent bundle TSO(3) associated with SO(3), where the torques implement the feedback control of relative attitudes and angular velocities. The Lyapunov-based almost global finite-time stability of the consensus subspace is demonstrated for both cases. Finally, numerical simulations are provided to verify the effectiveness of the proposed consensus control algorithms. 

This paper presents a finite-time stable (FTS) attitude tracking control scheme in discrete time for an unmanned vehicle. The attitude tracking control scheme guarantees discrete-time stability of the feedback system in finite time. This scheme is developed in discrete time as it is more convenient for onboard computer implementation and guarantees stability irrespective of sampling period. Finite-time stability analysis of the discrete-time tracking control is carried out using discrete Lyapunov analysis. This tracking control scheme ensures stable convergence of attitude tracking errors to the desired trajectory in finite time. The advantages of finite-time stabilization in discrete time over finite-time stabilization of a sampled continuous time tracking control system is addressed in this paper through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned vehicle model. 

Relative motion estimation of one rigid body with respect to another is a problem that has immediate applications to formations and maneuvers involving multiple unmanned vehicles or collision avoidance between vehicles. A finite-time stable observer for relative attitude estimation of a rigid object using onboard sensors on an unmanned vehicle, is developed and presented here. This observer assumes sensor inputs from onboard vision and inertial sensors, with the vision sensors measuring at least three points on the object whose relative locations with respect to a body-fixed frame on the object are also assumed to be known. In the absence of any measurement noise, the estimated relative attitude is shown to converge to the actual relative pose in a finite-time stable manner. Numerical simulations indicate that this relative attitude observer is robust to persistent measurement errors and converges to a bounded neighborhood of the true attitude.