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Classical gradient-based approximate dynamic programming approaches provide reliable and fast solution platforms for various optimal control problems. However, their dependence on accurate modeling approaches poses a major concern, where the efficiency of the proposed solutions are severely degraded in the case of uncertain dynamical environments. Herein, a novel online adaptive learning framework is introduced to solve action-dependent dual heuristic dynamic programming problems. The approach does not depend on the dynamical models of the considered systems. Instead, it employs optimization principles to produce model-free control strategies. A policy iteration process is employed to solve the underlying Hamilton–Jacobi–Bellman equation using means of adaptive critics, where a layer of separate actor-critic neural networks is employed along with gradient descent adaptation rules. A Riccati development is introduced and shown to be equivalent to solving the underlying Hamilton–Jacobi–Bellman equation. The proposed approach is applied on the challenging weight shift control problem of a flexible wing aircraft. The continuous nonlinear deformation in the aircraft’s flexible wing leads to various aerodynamic variations at different trim speeds, which makes its auto-pilot control a complicated task. Series of numerical simulations were carried out to demonstrate the effectiveness of the suggested strategy.

This paper presents a comparative study on the effects of grid resolution, vehicle velocity, and wind vector fields on the trajectory planning of unmanned airships. A wavefront expansion trajectory planner that minimizes a multi-objective cost function consisting of flight time, energy consumption, and collision avoidance while respecting the differential constraints of the vehicle is presented. Trajectories are generated using a variety of test environments and flight conditions to demonstrate that the inclusion of a high terrain map resolution, a temporal vehicle velocity, and a spatial wind vector field yields significant improvements in trajectory feasibility and energy economy when compared to trajectories generated using only two of these three elements.

Many tracking control solutions proposed in the literature rely on various forms of tracking error signals at the expense of possibly overlooking other dynamic criteria, such as optimizing the control effort, overshoot, and settling time, for example. In this article, a model-free control architectural framework is presented to track reference signals while optimizing other criteria as per the designer’s preference. The control architecture is model-free in the sense that the plant’s dynamics do not have to be known in advance. To this end, we propose and compare four tracking control algorithms which synergistically integrate a few machine learning tools to compromise between tracking a reference signal and optimizing a user-defined dynamic cost function. This is accomplished via two orchestrated control loops, one for tracking and one for optimization. Two control algorithms are designed and compared for the tracking loop. The first is based on reinforcement learning while the second is based on nonlinear threshold accepting technique. The optimization control loop is implemented using an artificial neural network. Each controller is trained offline before being integrated in the aggregate control system. Simulation results of three scenarios with various complexities demonstrated the effectiveness of the proposed control schemes in forcing the tracking error to converge while minimizing a pre-defined system-wide objective function.

This paper presents the kinematics of a planar multibody vehicle which is aimed at the exploration, data collection, non-destructive testing and general autonomous navigation and operations in confined environments such as pipelines. The robot is made of several identical modules hinged by passive revolute joints. Every module is actuated with four active revolute joints and can be regarded as a parallel mechanism on a mobile platform. The proposed kinematics allows to overcome the nonholonomic kinematic constraint, which characterizes typical wheeled robots, resulting into a higher number of degrees of freedom and therefore augmented actuation inputs. Singularities in the kinematics of the modules are analytically identified. We present the dimensional synthesis of the length of the arms obtained as the solution of an optimization problem with respect to a suitable dexterity index. Simulation results illustrate a kinematic control path following inside pipes. Critical scenarios such as 135° elbows and concentric restriction are explored. Path following shows the kinematic capability of deployment of the robot for autonomous operations in pipelines, with feedback implemented by on-board sensors.

The optimal tracking problem is addressed in the robotics literature by using a variety of robust and adaptive control approaches. However, these schemes are associated with implementation limitations such as applicability in uncertain dynamical environments with complete or partial model-based control structures, complexity and integrity in discrete-time environments, and scalability in complex coupled dynamical systems. An online adaptive learning mechanism is developed to tackle the above limitations and provide a generalized solution platform for a class of tracking control problems. This scheme minimizes the tracking errors and optimizes the overall dynamical behavior using simultaneous linear feedback control strategies. Reinforcement learning approaches based on value iteration processes are adopted to solve the underlying Bellman optimality equations. The resulting control strategies are updated in real time in an interactive manner without requiring any information about the dynamics of the underlying systems. Means of adaptive critics are employed to approximate the optimal solving value functions and the associated control strategies in real time. The proposed adaptive tracking mechanism is illustrated in simulation to control a flexible wing aircraft under uncertain aerodynamic learning environment.

Autonomous robotics has permeated several industrial, research and consumer robotic applications, of which path planning is an important component. The path planning algorithm of choice is influenced by the application at hand and the history of algorithms used for such applications. The latter is dependent on an extensive conglomeration and classification of path planning literature, which is what this work focuses on. Specifically, we accomplish the following: typical classifications of path planning algorithms are provided. Such classifications rely on differences in knowledge of the environment (known/unknown), robot (model-specific/generic), and constraints (static/dynamic). This classification however, is not comprehensive. Thus, as a resolution, we propose a detailed taxonomy based on a fundamental parameter of the space, i.e. its ability to be characterized as a set of disjoint or connected points. We show that this taxonomy encompasses important attributes of path planning problems, such as connectivity and partitioning of spaces. Consequently, path planning spaces in robotics may be viewed as simply a set of points, or as manifolds. The former can further be divided into unpartitioned and partitioned spaces, of which the former uses variants of sampling algorithms, optimization algorithms, model predictive controls, and evolutionary algorithms, while the latter uses cell decomposition and graph traversal, and sampling-based optimization techniques.This article achieves the following two goals: The first is the introduction of an all-encompassing taxonomy of robotic path planning. The second is to streamline the migration of path planning work from disciplines such as mathematics and computer vision to robotics, into one comprehensive survey. Thus, the main contribution of this work is the review of works for static constraints that fall under the proposed taxonomy, i.e., specifically under topology and manifold-based methods. Additionally, further taxonomy is introduced for manifold-based path planning, based on incremental construction or one-step explicit parametrization of the space.

Path planning is an intrinsic component of autonomous robotics, be it industrial, research or consumer robotics. Such avenues experience constraints around which paths must be planned. While the choice of an appropriate algorithm is application-dependent, the starting point of an ideal path planning algorithm is the review of past work. Historically, algorithms were classified based on the three tenets of autonomous robotics which are the ability to avoid different constraints (static/dynamic), knowledge of the environment (known/unknown) and knowledge of the robot (general/model specific). This division in literature however, is not comprehensive, especially with respect to dynamics constraints. Therefore, to remedy this issue, we propose a new taxonomy, based on the fundamental tenet of characterizing space, i.e., as a set of distinct, unrelated points or as a set of points that share a relationship. We show that this taxonomy is effective in addressing important parameters of path planning such as connectivity and partitioning of spaces. Therefore, path planning spaces may now be viewed either as a set of points or, as a space with structure. The former relies heavily on robot models, since the mathematical structure of the environment is not considered. Thus, the approaches used are variants of optimization algorithms and specific variants of model-based methods that are tailored to counteract effects of dynamic constraints. The latter depicts spaces as points with inter-connecting relationships, such as surfaces or manifolds. These structures allow for unique characterizations of paths using homotopy-based methods. The goals of this work, viewed specifically in light with dynamic constraints, are therefore as follows: First, we propose an all-encompassing taxonomy for robotic path planning literature that considers an underlying structure of the space. Second, we provide a detailed accumulation of works that do focus on the characterization of paths in spaces formulated to show underlying structure. This work accomplishes the goals by doing the following: It highlights existing classifications of path planning literature, identifies gaps in common classifications, proposes a new taxonomy based on the mathematical nature of the path planning space (topological properties), and provides an extensive conglomeration of literature that is encompassed by this new proposed taxonomy.

In this manuscript, an optimal time-varying P-controller is presented for a class of continuous-time underactuated nonlinear systems in the presence of process noise associated with systems’ inputs. This is a state feedback control strategy where the optimization is performed on a time-varying feedback operator (herein called the feedback control gain). The main goal of the current manuscript is to provide a framework for multi-input multi-output nonlinear systems which yields a satisfactory tracking performance based on the optimal time-varying feedback control gain. Unlike other feedback control techniques that perform dynamic linearization of system models, the proposed time-varying Pcontroller provides the full-state feedback control to the original nonlinear system model. Hence, this P-controller guarantees global asymptotic state-tracking. Furthermore, the bounded system’s process noise is taken into consideration to measure the controller’s robustness. The proposed P-controller is tested for its nonlinear trajectory tracking and fixed-point stabilization capabilities with two nonholonomic systems in the presence of input noise.

Autonomous robotic path planning in partially known environments, such as warehouse robotics, deals with static and dynamic constraints. Static constraints include stationary obstacles, robotic and environmental limitations. Dynamic constraints include humans, robots and dis/appearance of anticipated dangers, such as spills. Path planning consists of two steps: First, a path between the source and target is generated. Second, path segments are evaluated for constraint violation. Sampling algorithms trade memory for maximal map representation. Optimization algorithms stagnate at non-optimal solutions. Alternatively, detailed grid-maps view terrain/structure as expensive memory costs. The open problem is thus to represent only constraint-free, navigable regions and generating anticipatory/reactive paths to combat new constraints. To solve this problem, a Constraint-Free Discretized Manifolds-based Path Planner (CFDMPP) is proposed in this paper. The algorithm’s first step focuses on maximizing map knowledge using manifolds. The second uses homology and homotopy classes to compute paths. The former constructs a representation of the navigable space as a manifold, which is free of apriori known constraints. Paths on this manifold are constraint-free and do not have to be explicitly evaluated for constraint violation. The latter handles new constraint knowledge that invalidate the original path. Using homology and homotopy, path classes can be recognized and avoided by tuning a design parameter, resulting in an alternative constraint-free path. Path classes on the discretized constraint-free manifold characterize numerical uniqueness of paths around constraints. This designation is what allows path class characterization, avoidance, and querying of a new path class (multiple classes with tuning), even when constraints are simply anticipatory.

The aerodynamic model of flexible wing aircraft is highly nonlinear with continuously time-varying dynamics under kinematic constraints. The nonlinearities stem from the aerodynamic forces and continuous deformations in the flexible wing. In spite of the various experimental attempts and theoretical setups that were made to model these dynamics, an accurate formulation was not achieved. The control paradigms of the aircraft are concerned with the electro-mechanical coupling between the pilot and the wing. It is challenging to design a flight controller for such aircraft while complying with these constraints. In this paper, innovative machine learning technique is employed to design a robust online model-free control scheme for flexible wing aircraft. The controller maintains internal asymptotic stability for the aircraft in real-time using selected set of measurements or states in uncertain dynamical environment. It intelligently incorporates the varying dynamics, geometric parameters, and physical constraints of the aircraft into optimal control strategies. The adaptive learning structure employs a policy iteration approach, taking advantage of Bellman optimality principles, to converge to an optimal control solution for the problem. Artificial neural networks are adopted to implement the adaptive learning algorithm in real-time without prior knowledge of the aerodynamic model of the aircraft. The control scheme is generalized and shown to function effectively for different pilot/wing control mechanisms. It also demonstrated its ability to overcome the undesired stability problems caused by coupling the pilot’s dynamics with the flexible wing’s frame of motion.