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.
more »
« less
Trajectory generation on SE(3) with applications to a class of underactuated vehicles
This paper addresses the problem of generating
a continuous and differentiable trajectory on the Lie group of
rigid body motions, SE(3), for a class of underactuated vehicles
modeled as rigid bodies. The three rotational degrees of freedom
(DOF) are independently actuated, while only one translational
DOF is actuated by a body-fixed thrust vector. This model
is applicable to a large set of unmanned vehicles, including
fixed-wing and rotorcraft unmanned aerial vehicles (UAVs).
The formulation utilizes exponential coordinates to express the
underactuation constraint as an intrinsic part of the problem.
It provides steps to generate a rest-to-rest trajectory after
obtaining conditions that guarantee controllability. An attitude
trajectory is selected to satisfy the given initial and final attitude
state. The position trajectory generation is subsequently posed
as an optimal control problem expressed as a linear quadratic
regulator (LQR) in the exponential coordinates corresponding
to position. As a result, an optimal position trajectory is
obtained which ensures that the trajectory generated is feasible
with realistic velocities and with given initial pose and final
pose, while satisfying the underactuation constraint. Numerical
simulation results are obtained that validate this trajectory
generation scheme.
more »
« less
- Award ID(s):
- 1739748
- PAR ID:
- 10076908
- Date Published:
- Journal Name:
- 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
- Page Range / eLocation ID:
- 2557 to 2562
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
This paper addresses the problem of generating a position trajectory with pointing direction constraints at given waypoints for underactuated unmanned vehicles. The problem is initially posed on the configuration space ℝ 3 × ℝ 2 and thereafter, upon suitable modifications, is re-posed as a problem on the Lie group SE(3). This is done by determining a vector orthogonal to the pointing direction and using it as the vehicle's thrust direction. This translates to converting reduced attitude constraints to full attitude constraints at the waypoints. For the position trajectory, in addition to position constraints, this modification adds acceleration constraints at the waypoints. For real-time implementation with low computational expenses, a linear-quadratic regulator (LQR) approach is adopted to determine the position trajectory with smoothness upto the fourth time derivative of position (snap). For the attitude trajectory, the thrust direction extracted from the position trajectory is used to first propagate the attitude to the subsequent waypoint and then correct it over time to achieve the desired attitude at this waypoint. Finally, numerical simulation results are presented to validate the trajectory generation scheme.more » « less
-
This paper considers the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). A map is considered, characterized by a traffic intensity of users to be served. The UAV BS must travel from a given initial location at an initial time to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. The problem is formulated using the framework of Lagrangian mechanics. When the traffic intensity is quadratic (single-phase), we derive closed-form formulas for the optimal trajectory. When the traffic intensity is bi-phase, necessary conditions of optimality are provided and an Alternating Optimization Algorithm is proposed, that returns a trajectory satisfying these conditions. The Algorithm is initialized with a Model Predictive Control (MPC) online algorithm. Numerical results show how the trajectory is improved with respect to the MPC solution.more » « less
-
A framework for autonomous waypoint planning, trajectory generation through waypoints, and trajectory tracking for multi-rotor unmanned aerial vehicles (UAVs) is proposed in this work. Safe and effective operations of these UAVs is a problem that demands obstacle avoidance strategies and advanced trajectory planning and control schemes for stability and energy efficiency. To address this problem, a two-level optimization strategy is used for trajectory generation, then the trajectory is tracked in a stable manner. The framework given here consists of the following components: (a) a deep reinforcement learning (DRL)-based algorithm for optimal waypoint planning while minimizing control energy and avoiding obstacles in a given environment; (b) an optimal, smooth trajectory generation algorithm through waypoints, that minimizes a combinaton of velocity, acceleration, jerk and snap; and (c) a stable tracking control law that determines a control thrust force for an UAV to track the generated trajectory.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC.2017.8264029
