Real-Time 3D Guidance and Obstacle Avoidance for UxVs
The workshop is aimed at providing an insight into robust approach to generate feasible quasi-optimal trajectories for single and multiple unmanned vehicles (UxVs) based on the inverse dynamics in the virtual domain (IDVD) - a direct method of calculus of variations originally developed for a piloted combat aircraft. The proposed approach proved to be very suitable for the conceptual design, as well as modeling and simulation of different missions involving collaborative collision-free control of multiple heterogeneous vehicles. Also, it is one step away from converting a developed and tested algorithm into an executable code to be uploaded into the robot's computer to enable updating a reference trajectory at a 0.1-1Hz rate. Interactive Macromedia Flash tutorials are used to assist workshop participants in understanding underlying concepts. Examples of code developed in the MATLAB/Simulink development environment as well as an overview of on-line guidance algorithms for several unmanned platforms are presented and discussed. These platforms include spacecraft, missile, airplane, aerial delivery system, rotorcraft, and maritime vehicles.
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Tutorial schedule |
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| 09:00-10:45 | Onboard real-time trajectory generator. Problem formulation. Historical background and the essence of direct methods The workshop begins by formulating the most general optimal control problem as applied to onboard real-time trajectory generation for UxVs. It follows by synthesis and analysis of an optimal control structure derived from the Minimum Principle. The reference solution is developed and used to assess applicability of several direct-method-based approaches (collocation, transcription, pseudospecral) for real-time trajectory generation onboard a UxV. |
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| 11:00-12:30 | Choosing the basis functions and satisfying the boundary conditions Introduction to IDVD method starts from a discussion about different parameterizations of candidate trajectories in the virtual domain. The order of parametrization (that may employ monomials, polynomials and/or trigonometric functions) is defined by the number of boundary conditions, while flexibility of a candidate trajectory is determined by a few varied parameters. |
| lunch | |
| 14:00-15:30 | Space and time decoupling. Differential flatness and inverse dynamics. Practical examples This portion of workshop shows how variable mapping between the virtual and physical domains allows decoupling trajectory and speed profile optimization. Differential flatness of vehicle dynamics allows expressing all states and controls via the higher-order derivatives of an output vector, defined analytically. Gradient-free unconstrained minimization algorithm assures superb sub-first-order convergence of the optimization procedure. |
| break | |
| 15:45-17:00 | Six-degree-of-freedom kinematics and more practical examples The last part of workshop addresses more sophisticated case involving optimization of translational and rotational motion. The representative example addresses satellite transition and reorientation to satisfy the spatial and temporal constraints imposed by the problem of docking with a tumbling object. Discussion includes the development of a complete computational scheme utilizing the Bezier curves to approximate attitude dynamics. |
Oleg Yakimenko is a Professor at the Naval Postgraduate School, Monterey, CA, USA. He holds two Ph.D. degrees – in Aerospace Engineering and Operations Research – and is an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA).
