Robot Control Problem Research Articles

Nonlinear Optimal and Multi-Loop Flatness-Basedcontrol of Omnidirectional 3-Wheel Mobile Robots

In this article, the control problem for omnidirectional 3-wheel autonomous mobile robots is solved with the use of (i) a nonlinear optimal control method (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the omnidirectional 3-wheel autonomous mobile robots undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrix. The linearization point is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the omnidirectional 3-wheel autonomous mobile robot is separated into chained subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. The state variables of the preceding (i-th) subsystem become virtual control inputs for the subsequent (i+1-th) subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves trajectory tracking and autonomous navigation for the omnidirectional 3-wheel autonomous mobile robots without the need of diffeomorphisms and complicated state-space model transformations.

Adaptive neural network event-triggered secure formation control of nonholonomic mobile robots subject to deception attacks

This paper investigates the adaptive neural network (NN) event-triggered secure formation control problem for nonholonomic mobile robots (NMRs) subject to deception attacks. The NNs are employed to approximate unknown nonlinear functions in robotic dynamics. Since the transmission channel from sensor-to-controller is vulnerable to deception attacks, a NN estimation technique is introduced to estimate the unknown deception attacks. In order to alleviate the amount of communication between controller-and-actuator, an event-triggered mechanism with relative threshold strategy is established. Then, an adaptive NN event-triggered secure formation control method is proposed. It is proved that all closed-loop signals of controlled systems are bounded and the formation tracking errors converge a neighborhood of the origin in the presence of deception attacks. The comparative simulations illustrate the effectiveness of the proposed secure formation control scheme.

Balance Controller Design for Inverted Pendulum Considering Detail Reward Function and Two-Phase Learning Protocol

As a complex nonlinear system, the inverted pendulum (IP) system has the characteristics of asymmetry and instability. In this paper, the IP system is controlled by a learned deep neural network (DNN) that directly maps the system states to control commands in an end-to-end style. On the basis of deep reinforcement learning (DRL), the detail reward function (DRF) is designed to guide the DNN learning control strategy, which greatly enhances the pertinence and flexibility of the control. Moreover, a two-phase learning protocol (offline learning phase and online learning phase) is proposed to solve the “real gap” problem of the IP system. Firstly, the DNN learns the offline control strategy based on a simplified IP dynamic model and DRF. Then, a security controller is designed and used on the IP platform to optimize the DNN online. The experimental results demonstrate that the DNN has good robustness to model errors after secondary learning on the platform. When the length of the pendulum is reduced by 25% or increased by 25%, the steady-state error of the pendulum angle is less than 0.05 rad. The error is within the allowable range. The DNN is robust to changes in the length of the pendulum. The DRF and the two-phase learning protocol improve the adaptability of the controller to the complex and variable characteristics of the real platform and provide reference for other learning-based robot control problems.

Research on designing dynamic model of TITAN-VIII quadruped robot based on the robot structure

Quadruped robots have many advantages over wheeled robots in that they have high mobility and can move on any terrain. However, the control problem of four-legged robots will be more complicated because the robot's kinematic model has a high order and the dynamic process is complicated, so it is necessary to implement order reduction methods when constructing kinematic equations for four-legged robots. The article proposes a simplified method to determine the kinematic equations for four-legged robots called TITAN-VIII. The Denavit-Hartenberg (D-H) rule is used to analyze the forward kinematics. The inverse kinematic equations are determined on the basis of mathematics and the structure of the robot's legs. The research results are simulated on MATLAB Simulink software.

Deep Koopman-operator-based model predictive control for free-floating space robots with disturbance observer

This paper investigates the optimal tracking control problem of free-floating space robots in the presence of non-ideal factors, such as model uncertainties and external disturbances. To address this issue, we first leverage the deep Koopman operator, facilitated with a deep neural network, to establish an offline formulation of a global linearization model for a micro-nano free-floating space robot. Based on the estimated linearization model, we then employ the model predictive control method for online optimization control, achieving a significantly reduced computational burden. Additionally, a decay factor is integrated into the model predictive control optimization objective function to balance the precision of joint angles tracking with the suppression of base satellite attitude disturbance. To further address the modeling inaccuracies and external disturbances, we incorporate a disturbance observer based on a radial basis function neural network for online compensation within the model predictive control framework. This augmentation enhances tracking precision and robustness. Several groups of simulation results are carried out to demonstrate the effectiveness of the proposed method, showing its capability of energy consumption, disturbance rejection and enhanced robustness. These highlight the potential of the proposed method to improve the control performance of free-floating space robots, even in the absence of a precise dynamic model.

Solving Advanced Missile Robotic Control Problem Via Integral Rohit transform

The problem of robotic control of an advanced missile requires designing control systems for remote-controlled missiles with sufficient abilities. These control systems need to handle navigation, guidance, propulsion, and potentially other tasks like target acquisition and avoidance of obstacles. The various aspects of missile dynamics are described by complex and non-linear differential equations. Due to this, it becomes difficult to obtain their analytical solutions. During system design and analysis, to solve these complex and non-linear differential equations, numerical techniques like Euler’s technique, the Runge-Kutta technique, or more advanced mathematical techniques are generally used. The advanced missile robotic control problem is one of the problems represented by second-order linear differential equations. In this paper, the integral Rohit transform (RT) has been applied to solve an advanced missile robotic control problem. This transformation has never been applied in working out the advanced missile robotic control problem. This paper applies a new technique for solving the second-order linear differential equation representing the advanced missile robotic control problem to obtain its required turn angle so that it will be able to catch and destroy the attacker. The necessary graphs are plotted to illustrate the numerical solution of the robotic control of an advanced missile. It reveals that the integral Rohit transform (RT) technique is an effective technique to solve the advanced missile robotic control problem.

Adaptive neural network-based practical predefined-time nonsingular terminal sliding mode control for upper limb rehabilitation robots

This article investigates the predefined time trajectory tracking control problem of upper limb rehabilitation robots in the presence of the model uncertainty and external disturbances. An adaptive neural network-based practical predefined-time fast nonsingular terminal sliding-mode control (PPT-FNTSMC) strategy is proposed, in which a novel sliding mode surface is constructed to achieve predefined-time convergence and avoid the singularity problem as well. Additionally, a neural network is employed to approximate the lumped disturbances, and the estimated values are utilized in the controller for compensation, thereby reducing the required switching gain and mitigating chattering phenomenon. A rigorous theoretical analysis is provided to illustrate that the tracking errors can converge to a vicinity of the origin in a predefined time. Finally, simulations on a two-joint single-arm robot and a 5-DOF upper-limb exoskeleton are conducted and compared with an existing control method to demonstrate the effectiveness and superiority of the proposed control strategy.

Novel Adaptive Control for Flexible-Joint Robots With Unknown Measurement Sensitivity

For the existing tracking control schemes of flexible-joint robots, precise sensor measurement is an implicit premise. However, idealized sensors are difficult to achieve due to manufacturing technology or other external factors. To this end, this paper further investigates the tracking control problem for flexible-joint robots with unknown measurement sensitivity. Specifically, for such multi-input multi-output Euler-Lagrange systems with completely unknown system dynamics, a novel measurement values-based adaptive control method is proposed by fusing sensitivity information and system variables into Lyapunov function candidates, where the restriction on system states in other the approximation lemma-based results is removed, since unknown nonlinearities are scaled by the structural characteristics of system variables. Above all, even if there are measurement errors, satisfactory tracking performance can be obtained by adjusting the design parameters, which is proved by rigorous theoretical analysis. Finally, hardware experiments further verify the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the trajectory tracking control problem for flexible-joint robots under imprecise sensor measurements. Due to manufacturing technology limitations and component aging, there is inevitably a deviation between the measured values of sensors and real values, and this problem may become more prominent as the working environment of flexible-joint robots tends to become more complex. To our knowledge, most of the existing solutions for flexible-joint robots are developed based on precise sensor measurements, and they may fail to achieve satisfactory performance when real state information is not available. Moreover, the prior knowledge about model parameters and measurement sensitivity is difficult or impossible to exactly obtain in practice, which seriously hinders the further application of control methods that are dependent on system dynamics. To this end, this paper proposes a novel tracking control scheme based on measurement information for flexible-joint robots with unknown measurement sensitivity, where the dependence on model information is eliminated with the elaborately constructed Lyapunov function candidates, and the real tracking error is still adjusted to an acceptable range even if there are measurement errors. Preliminary experiments on a flexible-joint robot developed by Quanser company demonstrate the feasibility and effectiveness of the proposed method. In future studies, designing an effective scheme to achieve direct preset tracking control is the focus of the work.

Sequential control barrier functions for mobile robots with dynamic temporal logic specifications

We address a motion planning and control problem for mobile robots to satisfy rich, time-varying tasks expressed as Signal Temporal Logic (STL) specifications. The specifications may include tasks with nested temporal operators or time-conflicting requirements (e.g., achieving periodic tasks or tasks defined within the same time interval). Moreover, the tasks can be defined in locations changing with time (i.e., dynamic targets), and their future motions are not known a priori. This unpredictability requires an online control approach which motivates us to investigate the use of control barrier functions (CBFs). The proposed CBFs take into account the actuation limits of the robots and a feasible sequence of STL tasks. They define time-varying feasible sets of states the system must always stay inside. We show the feasible sequence generation process that even includes the decomposition of periodic tasks and alternative scenarios due to disjunction operators. The sequence is used to define CBFs, ensuring STL satisfaction. We also show some theoretical results on the correctness of the proposed method. We illustrate the benefits of the proposed method and analyze its performance via simulations and experiments with aerial robots.

Solving Problem of Robotic Control of Advanced Missile Via Integral Gupta Transform

Solving Problem of Robotic Control of Advanced Missile Via Integral Gupta Transform

A Perspective on Cognitive Robot Research and Development

The purpose of this paper is to present my personal journey in the last 30-plus years of research and development efforts on a cognitive robotic system called Intelligent Soft Arm Control (ISAC). In doing so, I will highlight how our team approached solving certain robot intelligence, communication, and control problems.

Task-oriented safety field for robot control in human-robot collaborative assembly based on residual learning

With the development of smart manufacturing, human-robot collaboration (HRC) is seen as the future of manufacturing. In a manufacturing environment with HRC, safety has been raising significant attention since the conventional separation of workspaces between robots and humans is removed. In this paper, a dynamic safety field is constructed that takes into account the collaborative assembly task requirements and the motions of both humans and robots. This safety field guides robot actions, ensuring that the robot carries out the required tasks while maintaining a safe distance from human workers. Based on the task requirements and safety considerations between humans and robots, a robot motion planning and control problem is formulated. To solve this problem, a hybrid RRL control scheme is proposed where a residual reinforcement learning (RRL) method is developed to combine the safety field-based control method with a deep reinforcement learning (DRL) method. Numerical studies are conducted to evaluate the performance of the proposed, which is compared with a pure deep Q-network (DQN) based method and a rapidly exploring random tree (RRT) method. The simulation results show that the proposed method can effectively optimize robot trajectories and outperforms the DQN-based and the RRT method in terms of computational efficiency.

A Springy Leg and a Double Backflip

This paper presents a simulation study of a planar monopod robot's motion search and control problems. The robot's passively spring-loaded prismatic joint in the lower body (between the foot and the shin) assists it in performing athletic motions. Systems of this kind can balance on a single point, hop, and produce complex movements with a suitable control strategy. We aim to investigate the application of direct orthogonal collocation (DOC) methods to nonlinear motion search problems for obtaining the continuity accuracy of using an ODE solver but exploiting the faster computation and convergence of collocation methods. Moreover, the presented controller allows the robot to get up from the ground, move to the ready position, and replicate the optimized motion (a double backflip) in a dynamic simulation.

Formation Control of Networked Mobile Robots With Unknown Reference Orientation

In this article, the distributed leader-following formation control problem of networked mobile robots is investigated. The desired formation is specified by a reference trajectory generated by the leader and the followers' desired relative positions with respect to the leader. On the one hand, for any security-aware multirobot systems, the values of the leader's position and orientation are generally not allowed to be transmitted via the inter-robot communication in the case of the information leakage of formation caused by the possible eavesdropping. On the other hand, relative orientations, different from relative positions, are typically difficult for mobile robots to measure directly, which makes the reference orientation unknown to all followers. In order to track the reference trajectory and form a desired formation in the absence of the reference orientation, followers are divided into two groups according to whether they are able to directly measure the relative positions with respect to the leader. The topology of the sensing/communication network among multirobot systems is described by a directed graph containing a directed spanning tree. Then, two observer-based control laws are proposed for two groups of followers, respectively, in both of which the unknown tracking errors are properly estimated. It is rigorously proven that the resulting closed-loop multirobot system is globally uniformly asymptotically stable. Finally, the effectiveness of our approach is illustrated by an experiment conducted on networked TurtleBot3 Burger mobile robots.

Interactive Evolutionary Multiobjective Optimization via Learning to Rank

In practical multi-criterion decision-making, it is cumbersome if a decision maker (DM) is asked to choose among a set of trade-off alternatives covering the whole Pareto-optimal front. This is a paradox in conventional evolutionary multi-objective optimization (EMO) that always aim to achieve a well balance between convergence and diversity. In essence, the ultimate goal of multi-objective optimization is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory trade-offs among multiple conflicting criteria. Bearing this in mind, this paper develops a framework for designing preference-based EMO algorithms to find SOI in an interactive manner. Its core idea is to involve human in the loop of EMO. After every several iterations, the DM is invited to elicit her feedback with regard to a couple of incumbent candidates. By collecting such information, her preference is progressively learned by a learning-to-rank neural network and then applied to guide the baseline EMO algorithm. Note that this framework is so general that any existing EMO algorithm can be applied in a plug-in manner. Experiments on 48 benchmark test problems with up to 10 objectives and a real-world multi-objective robot control problem fully demonstrate the effectiveness of our proposed algorithms for finding SOI.

A viscosity-type scheme for optimization problems in Hadamard spaces with applications

In this article, we propose a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multi-valued nonexpansive mapping in the framework of Hadamard spaces. We obtain a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fréchet mean, find the mean of probabilities, minimize energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature.

Direct multiple shooting and direct collocation perform similarly in biomechanical predictive simulations

Direct multiple shooting (DMS) and direct collocation (DC) are two standard transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have yet to be compared in terms of solution and speed. Through five examples of predictive simulations solved using five transcription methods and 100 initial guesses in the Bioptim software, we showed that no single method outperformed the others systematically. All methods converged to almost the same solution (cost, states, and controls) in all but one OCP, with several local minima found in the latter. Nevertheless, DC based on fourth-order Legendre polynomials provided overall better results, especially regarding dynamics integration accuracy compared to DMS based on a fourth-order Runge–Kutta method. Furthermore, expressing the rigid-body constraints using inverse dynamics was usually faster than forward dynamics. DC with dynamic constraints based on inverse dynamics converged to better and less variable solutions. We recommend starting with this transcription to solve OCPs but keep testing other methods.

Safe Control With Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control

Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies—these certificates provide concise data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned controller but also provide supervision during training, allowing safety and stability requirements to influence the training process itself. In this article, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this article will serve as an accessible introduction to the theory and practice of certificate learning, both to those who wish to apply these tools to practical robotics problems and to those who wish to dive more deeply into the theory of learning for control.

Decentralized Circular Formation Control of Nonholonomic Mobile Robots Under a Directed Sensor Graph

This paper investigates the circular formation control problem of multiple unicycle-type mobile robots under a directed sensor graph. The topology of the sensor graph among all robots is described by a directed graph containing a spanning tree, and the node denoting the center is only required to be globally reachable in the sensor graph. A dynamic control law is developed such that the multi-robot systems with speed constraint are able to globally converge to a circular formation prescribed by a stationary center, a radius, and a spacing configuration. Remarkably, the proposed control law does not rely on any communication, and only requires each robot to use local measurements with respect to its neighbors based on its local coordinate frame, which makes it feasible to implement this control law in a decentralized manner. The global asymptotic stability of the closed-loop multi-robot systems is established by small gain theorem of which the small-gain condition is guaranteed by a low gain parameter in the designed observer.

Policy ensemble gradient for continuous control problems in deep reinforcement learning

Policy gradient algorithms for reinforcement learning (RL) have successfully tackled a broad range of high-dimensional continuous RL problems, including many challenging robotic control problems. These algorithms can be largely divided into two categories, i.e., on-policy algorithms and off-policy algorithms. Off-policy deep RL (DRL) algorithms enjoy better sample efficiency than and often outperform on-policy algorithms. However, cutting-edge off-policy algorithms still suffer from the low-quality estimation of policy gradients, resulting in compromised learning performance and high sensitivity to hyper-parameter settings. To address this issue, we propose a new concept of robust policy gradient (RPG). Driven by RPG, this paper further develops a new policy ensemble gradient (PEG) algorithm for DRL, inspired by the recent success of several ensemble DRL algorithms. PEG efficiently and effectively estimates RPG by using multiple policy gradients obtained respectively from several off-policy base learners in an ensemble. The estimated RPG is then utilized for training all base learners simultaneously. Comprehensive experiments have been performed on six Mujoco benchmark problems. Compared to four state-of-the-art off-policy algorithms and four cutting-edge ensemble policy gradient algorithms, our new PEG algorithm achieved highly competitive stability, performance and sample efficiency. Further analysis shows that PEG is insensitive to varied hyper-parameter settings, confirming the positive role of RPG in building reliable and effective off-policy DRL algorithms.