Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its strength lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonlinear, its equivalent convex formulation is proposed utilizing state-dependent coefficient parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L₂-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H∞, and given nonlinear control for spacecraft attitude control and synchronization problems

A Nonlinear Optimal Control Approach for a Lower-Limb Robotic Exoskeleton

The use of robotic limb exoskeletons is growing fast either for rehabilitation purposes or in an aim to enhance human ability for lifting heavy objects or for walking for long distances without fatigue. The paper proposes a nonlinear optimal control approach for a lower-limb robotic exoskeleton. The method has been successfully tested so far on the control problem of several types of robotic manipulators and this paper shows that it can also provide an optimal solution to the control problem of limb robotic exoskeletons. To implement this control scheme, the state-space model of the lower-limb robotic exoskeleton undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator

Feasible Policy Iteration

Safe reinforcement learning (RL) aims to solve an optimal control problem under safety constraints. Existing $\textit{direct}$ safe RL methods use the original constraint throughout the learning process. They either lack theoretical guarantees of the policy during iteration or suffer from infeasibility problems. To address this issue, we propose an $\textit{indirect}$ safe RL method called feasible policy iteration (FPI) that iteratively uses the feasible region of the last policy to constrain the current policy. The feasible region is represented by a feasibility function called constraint decay function (CDF). The core of FPI is a region-wise policy update rule called feasible policy improvement, which maximizes the return under the constraint of the CDF inside the feasible region and minimizes the CDF outside the feasible region. This update rule is always feasible and ensures that the feasible region monotonically expands and the state-value function monotonically increases inside the feasible region. Using the feasible Bellman equation, we prove that FPI converges to the maximum feasible region and the optimal state-value function. Experiments on classic control tasks and Safety Gym show that our algorithms achieve lower constraint violations and comparable or higher performance than the baselines

Prohibited Volume Avoidance for Aircraft

This thesis describes the development of a pilot override control system that prevents aircraft entering critical regions of space, known as prohibited volumes. The aim is to prevent another 9/11 style terrorist attack, as well as act as a general safety system for transport aircraft. The thesis presents the design and implementation of three core modules in the system; the trajectory generation algorithm, the trigger mechanism for the pilot override and the trajectory following element. The trajectory generation algorithm uses a direct multiple shooting strategy to provide trajectories through online computation that avoid pre-defi ned prohibited volume exclusion regions, whilst accounting for the manoeuvring capabilities of the aircraft. The trigger mechanism incorporates the logic that decides the time at which it is suitable for the override to be activated, an important consideration for ensuring that the system is not overly restrictive for a pilot. A number of methods are introduced, and for safety purposes a composite trigger that incorporates di fferent strategies is recommended. Trajectory following is best achieved via a nonlinear guidance law. The guidance logic sends commands in pitch, roll and yaw to the control surfaces of the aircraft, in order to closely follow the generated avoidance trajectory. Testing and validation is performed using a full motion simulator, with volunteers flying a representative aircraft model and attempting to penetrate prohibited volumes. The proof-of-concept system is shown to work well, provided that extreme aircraft manoeuvres are prevented near the exclusion regions. These hard manoeuvring envelope constraints allow the trajectory following controllers to follow avoidance trajectories accurately from an initial state within the bounding set. In order to move the project closer to a commercial product, operator and regulator input is necessary, particularly due to the radical nature of the pilot override system

An Optimization approach to plant-controller co-design

Improving the behavior of a controlled mechanical device is traditionally accomplished by manipulating the parameters of the control system in isolation. If permitted, a better solution can be achieved by including the physical attributes of the mechanical structure as optimization variables. However, this expansion of the search space increases the importance of properly formulating the optimization problem to avoid undesirable behavior. Some modern (e.g. H∞) methods can be used to simultaneously optimize dynamic performance and robustness, but they require high levels of understanding and do not handle nonlinearities and arbitrary optimization constraints without additional augmentation. This work proposes and applies a method to add robustness to an optimized stabilizing controller and plant combination using constrained performance index optimization of chirp signal tracking. Using a chirp reference helps to improve the generality of the system response and ensures that resonant modes lay outside the useful range of input frequencies. Moreover, applying constraints on physical optimization parameters and their sensitivities helps to limit the solution space of a potentially high-dimensional problem while ensuring that the resultant system is both realizable and robust. An experimental platform for studying the process of toner ink fusion was modeled to demonstrate the effectiveness of the proposed method. For this system, combined optimization resulted in a performance index over 45% better than the result of optimizing the controller alone. Meanwhile, a worst-case robustness floor was maintained on several critical and uncertain system qualities

Realtime Motion Planning for Manipulator Robots under Dynamic Environments: An Optimal Control Approach

This report presents optimal control methods integrated with hierarchical control framework to realize real-time collision-free optimal trajectories for motion control in kinematic chain manipulator (KCM) robot systems under dynamic environments. Recently, they have been increasingly used in applications where manipulators are required to interact with random objects and humans. As a result, more complex trajectory planning schemes are required. The main objective of this research is to develop new motion control strategies that can enable such robots to operate efficiently and optimally in such unknown and dynamic environments. Two direct optimal control methods: The direct collocation method and discrete mechanics for optimal control methods are investigated for solving the related constrained optimal control problem and the results are compared. Using the receding horizon control structure, open-loop sub-optimal trajectories are generated as real-time input to the controller as opposed to the predefined trajectory over the entire time duration. This, in essence, captures the dynamic nature of the obstacles. The closed-loop position controller is then engaged to span the robot end-effector along this desired optimal path by computing appropriate torque commands for the joint actuators. Employing a two-degree of freedom technique, collision-free trajectories and robot environment information are transmitted in real-time by the aid of a bidirectional connectionless datagram transfer. A hierarchical network control platform is designed to condition triggering of precedent activities between a dedicated machine computing the optimal trajectory and the real-time computer running a low-level controller. Experimental results on a 2-link planar robot are presented to validate the main ideas. Real-time implementation of collision-free workspace trajectory control is achieved for cases where obstacles are arbitrarily changing in the robot workspace

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored