Simplex Control Methods for Robust Convergence of Small Unmanned Aircraft Flight Trajectories in the Constrained Urban Environment

Constrained optimal control problems for Small Unmanned Aircraft Systems (SUAS) have long suffered from excessive computation times caused by a combination of constraint modeling techniques, the quality of the initial path solution provided to the optimal control solver, and improperly defining the bounds on system state variables, ultimately preventing implementation into real-time, on-board systems. In this research, a new hybrid approach is examined for real-time path planning of SUAS. During autonomous flight, a SUAS is tasked to traverse from one target region to a second target region while avoiding hard constraints consisting of building structures of an urban environment. Feasible path solutions are determined through highly constrained spaces, investigating narrow corridors, visiting multiple waypoints, and minimizing incursions to keep-out regions. These issues are addressed herein with a new approach by triangulating the search space in two-dimensions, or using a tetrahedron discretization in three-dimensions to define a polygonal search corridor free of constraints while alleviating the dependency of problem specific parameters by translating the problem to barycentric coordinates. Within this connected simplex construct, trajectories are solved using direct orthogonal collocation methods while leveraging navigation mesh techniques developed for fast geometric path planning solutions. To illustrate two-dimensional flight trajectories, sample results are applied to flight through downtown Chicago at an altitude of 600 feet above ground level. The three-dimensional problem is examined for feasibility by applying the methodology to a small scale problem. Computation and objective times are reported to illustrate the design implications for real-time optimal control systems, with results showing 86% reduction in computation time over traditional methods

Computer Architectures to Close the Loop in Real-time Optimization

© 2015 IEEE.Many modern control, automation, signal processing and machine learning applications rely on solving a sequence of optimization problems, which are updated with measurements of a real system that evolves in time. The solutions of each of these optimization problems are then used to make decisions, which may be followed by changing some parameters of the physical system, thereby resulting in a feedback loop between the computing and the physical system. Real-time optimization is not the same as fast optimization, due to the fact that the computation is affected by an uncertain system that evolves in time. The suitability of a design should therefore not be judged from the optimality of a single optimization problem, but based on the evolution of the entire cyber-physical system. The algorithms and hardware used for solving a single optimization problem in the office might therefore be far from ideal when solving a sequence of real-time optimization problems. Instead of there being a single, optimal design, one has to trade-off a number of objectives, including performance, robustness, energy usage, size and cost. We therefore provide here a tutorial introduction to some of the questions and implementation issues that arise in real-time optimization applications. We will concentrate on some of the decisions that have to be made when designing the computing architecture and algorithm and argue that the choice of one informs the other

Asymptotically Optimal Stabilizing Quadratic Control of an Inverted Pendulum

A new method for the design and synthesis of near-optimal, non linear control law is examined, based on a generalisation of LQ optimal control theory and which effectively provides a near-optimal gain schedule. The method is simple to apply and affords greater design flexibility (via state-dependent weighting) than conventional approaches. The resulting regulator can, in principle, be implemented in real-time owing to the casual nature of the required computations. However, the need to solve an algebraic Riccati equation at every time- point is burdensome and a number of algorithms that would permit parallel computation is discussed. The problem of stabilizing an inverted pendulum is used to illustrate the method and proves an exacting task that highlights a number of issues

Synthesis of the neuro-fuzzy regulator with genetic algorithm

Real-acting objects are characterized by the presence of various types of random perturbations, which significantly reduce the quality of the control process, which determines the use of modern methods of intellectual technology to solve the problem of synthesis of control systems of structurally complex dynamic objects, allowing to compensate the influence of external factors with the properties of randomness and partial uncertainty. The article considers issues of synthesis of the automatic control system of dynamic objects by applying the theory of intelligent control. In this case, a neural network based on radial-basis functions is used at each discrete interval for neuro-fuzzy approximation of the control system, allowing real-time adjustment of the regulator parameters. The radial basis function is designed to approximate functions defined in the implicit form of pattern sets. The neuro-fuzzy regulator's parameter configuration is accomplished using a genetic algorithm, enabling more efficient computation to determine the regulator's set parameters. The regulator's parameters are represented as a vector, facilitating their application to multidimensional objects. To determine the optimal tuning parameters of the neuro-fuzzy regulator, characterized by high convergence and the possibility of determining global extrema, a genetic algorithm was used. The effectiveness of the neuro-fuzzy regulator is explained by the possibility of providing quality control of the dynamic object under random perturbations and uncertainty of input data

Real-time experimental implementation of predictive control schemes in a small-scale pasteurization plant

Model predictive control (MPC) is one of the most used optimization-based control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary-game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multi-variable case study show a comparison between the system performance obtained with static and dynamical tuning.Peer ReviewedPostprint (author's final draft

Evolutionary-game-based dynamical tuning for multi-objective model predictive control

Model predictive control (MPC) is one of the most used optimization-based control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary-game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multi-variable case study show a comparison between the system performance obtained with static and dynamical tuning.Peer ReviewedPostprint (author's final draft

A Novel Collision Avoidance Logic for Unmanned Aerial Vehicles Using Real-Time Trajectory Planning

An effective collision avoidance logic should prevent collision without excessive alerting. This requirement would be even more stringent for an automatic collision avoidance logic, which is probably required by Unmanned Aerial Vehicles to mitigate the impact of delayed or lost link issues. In order to improve the safety performance and reduce the frequency of false alarms, this thesis proposes a novel collision avoidance logic based on the three-layer architecture and a real-time trajectory planning method. The aim of this thesis is to develop a real-time trajectory planning algorithm for the proposed collision avoidance logic and to determine the integrated logic’s feasibility, merits and limitations for practical applications. To develop the trajectory planning algorithm, an optimal control problem is formulated and an inverse-dynamic direct method along with a two stage, derivative-free pattern search method is used as the solution approach. The developed algorithm is able to take into account the flyability of three dimensional manoeuvres, the robustness to the intruder state uncertainty and the field-of-regard restriction of surveillance sensors. The testing results show that the standalone executable of the algorithm is able to provide a flyable avoidance trajectory with a maximum computation time less than 0.5 seconds. To evaluate the performance of the proposed logic, an evaluation framework for Monte Carlo simulations and a baseline approach for comparison are constructed. Based on five Monte Carlo simulation experiments, it is found that the proposed logic should be feasible as 1) it is able to achieve an update rate of 2Hz, 2) its safety performance is comparable with a reference requirement from another initial feasibility study, and 3) despite a 0.5 seconds computation latency, it outperforms the baseline approach in terms of safety performance and robustness to sensor and feedback error