Udwadia-Kalaba Approach Research Articles

Formation control of networked mobile robots with weighted directed topology using the Udwadia–Kalaba approach

Formation control of networked mobile robots with weighted directed topology using the Udwadia–Kalaba approach

A Novel Approach for Trajectory Tracking Control of an Under-Actuated Quad-Rotor UAV

A novel Udwadia-Kalaba approach for the trajectory tracking control of an under-actuated quad-rotor unmanned aerial vehicle (UAV) is presented. Compared to standard control approaches, the desired trajectories are treated as constraints called trajectory tracking constraints in this approach. Neither making any approximations or linearization of the nonlinear system nor imposing any a priori structure on the nature of the nonlinear controller, this methodology provides closedform nonlinear control. The control inputs satisfying the desired trajectory requirements can be obtained explicitly in compact closed form by solving Udwadia-Kalaba equation. Nonlinear dynamics modeling of a quad-rotor UAV is processed and a desired trajectory is given in this paper to illustrate this approach. The theoretical analysis and MATLAB simulation results verify the validity and efficiency of this approach. The real-time servo constraint forces are obtained conveniently and the quad-rotor UAV's movement meets the designed trajectory precisely.

An improved Udwadia–Kalaba approach for controller design in underactuated mechanical systems

An improved Udwadia–Kalaba approach for controller design in underactuated mechanical systems

Constraint-following control for dynamic systems with comprehensive constraints: the generalized Udwadia–Kalaba approach

Abstract A novel Generalized Udwadia-Kalaba (GUK) control method is proposed in this paper to effectively deal with the constraint-following problem with comprehensive constraints, be it equality constraints or inequality constraints. Fully considering the complex application scenario in practice which encompassed both clear and feasible trajectory, the equality constraints and inequality constraints are simultaneously applied to design rational and reliable controller. Specifically, a state transformation function is introduced to describe the inequality constraints. Further, the dynamic model with comprehensive constraints is established based on the GUK theory. Then, a corresponding constraint-following control is presented to render the system performance, uniform boundedness and uniform ultimate boundedness. The effectiveness of the GUK control is verfied by the stability analysis based on Lyapunov minimax approach and experimental verification of unmanned underwater vehicle (UUV). The desired control performances of UUV, constraint-following and collision avoidance, can be achieved. As an illustrative application, the UUV is designed to navigate through narrow sea trenches. Meanwhile, through comparative analysis with the linear quadratic regulator (LQR) method and Udwadia-Kalaba (UK) method, the superiority of this approach is demonstrated.

A Novel Trajectory Tracking Control of AGV Based on Udwadia-Kalaba Approach

Several control approaches have been used in order to achieve the trajectory tracking control of automated guided vehicle (AGV). But they are all based on the D'Alembert principle which requires to determine the Lagrangian multipliers. Unlike those control methods, in this paper, a novel approach of trajectory tracking control is presented, which is based on Udwadia-Kalaba approach. This approach presents a novel, concise and explicit equation of motion for constrained mechanical systems with holonomic and/or nonholonomic constraints as well as constraints that may be ideal or non-ideal. The Udwadia-Kalaba equation is uncoupled and free from the Lagrangian multipliers. In this paper, we classify constraints into structural constraints and performance constraints. Structural constraints are set up regardless of trajectory control and we use structural constraints to establish the dynamic model. Then the desired trajectory is set as performance constraints and constraint torques are solved by analyzing Udwadia-Kalaba equation. For AGV, a nonholonomic mechanical system, second-order constraints are used to get constraint forces and the numerical simulation is conducted by using Matlab. The results show that the AGV's movement meets the requirement and the tracking trajectory is exact and perfect. Compared with other approaches, this approach requires very little computation. Through two cases of tracking a circle and a line, how to use Udwadia-Kalaba equation to realize trajectory tracking control is shown in detail.

Distributed Formation-Containment Control of Networked Mobile Robots Using the Udwadia–Kalaba Approach

Distributed Formation-Containment Control of Networked Mobile Robots Using the Udwadia–Kalaba Approach

Robust approximate constraint-following control design based on Udwadia–Kalaba approach and experimental validation for the joint module of cooperative robot

Robust approximate constraint-following control design based on Udwadia–Kalaba approach and experimental validation for the joint module of cooperative robot

Human–Machine Shared Steering Control Under High-Speed Emergency Obstacle Avoidance Scenarios

The allocation of controlling and driving authority is an important and difficult aspect of human–machine shared steering control (SSC). This paper addresses the SSC problem in high-speed emergency obstacle avoidance scenarios. A parallel SSC framework containing a dynamic driving authority allocation model and a path tracking controller is developed, where the human driver and controller can control the vehicle simultaneously. First, fuzzy logic is adopted in the SSC framework to actively adjust the driving authority between the human driver and the controller. The driver steering state and path tracking error are considered to reduce the negative impact of a driver’s mis-operation and weaken any human–machine conflict. Subsequently, the path tracking controller in the proposed SSC system is designed based on a nonlinear vehicle lateral model to improve the accuracy of the controller, particularly when the vehicle is facing large lateral acceleration. To address the nonlinear control problem, the Udwadia–Kalaba approach is employed and the Lyapunov stability of the controller is proved. Finally, the effectiveness of the proposed SSC system is proved through simulation results, which show that the vehicle has excellent path tracking performance in high-speed obstacle avoidance scenarios. In addition, the system can resolve the human–machine conflict problem.

Formation tracking of multi-robot systems with switching directed topologies based on Udwadia-Kalaba approach

In this paper, a distributed formation tracking protocol is proposed for multi-robot systems with switching directed topologies based on the Udwadia-Kalaba approach. The basic idea is to use the consensus-based scheme to reconstruct formation tracking control requirement into a second-order constraint first, and then apply the Udwadia-Kalaba approach to obtain the constraint force required to achieve the formation tracking, and afterward derive the explicit equations of motion for the constrained multi-robot systems for the control algorithm design. The convergence analysis of the tracking error system is conducted to affirm that the proposed control algorithm can achieve the formation tracking when the switching directed topologies have a directed spanning tree across each switching time interval. Numerical simulations are performed to validate the effectiveness of the proposed algorithm.

Distributed formation control of networked mobile robots from the Udwadia–Kalaba approach

AbstractIn this article, formation control of networked mobile robots is studied. Two control strategies for the leaderless case and the leader‐following case are developed from the Udwadia–Kalaba approach, respectively. Differing from the existing results about formation control, which focus on kinematic models of robots, this article considers dynamic models and obtained a lower‐cost control force. To improve the robustness of the communication network, two distributed formation controllers are designed by establishing distributed estimators. Different from the centralized controllers, the distributed controllers established here only require local information, thus save communication resources and improve system robustness. Finally, some numerical simulations are provided to demonstrate the proposed methods are effective and have lower control cost.

Motion control of connected and automated vehicles in a lane‐changing scenario with guaranteed tracking performance

AbstractThe coupled, nonlinear vehicle dynamics and multi‐vehicle cooperative strategies make the lane‐changing maneuver control of vehicle platoons a challenging task. This paper presents the dynamic modeling and motion control of connected and automated vehicles (CAVs) for lane‐changing maneuver, utilizing the ideology of constraint‐following servo control. To guarantee a transient and steady tracking performance, a series of equality constraints and bilateral inequality constraints bounded by decaying functions or scalar constants are imposed on the dynamic state to formulate a constrained dynamical system. Since the original Udwadia‐Kalaba (UK) approach cannot handle inequality constraints and underactuated systems, a creative diffeomorphism method is applied to transform the bounded state into an unbounded one. Then, based on the UK approach and Lyapunov stability theory, a novel constraint‐following controller is designed to render the transformed states asymptotically stable in a full actuated system, and to achieve uniform stability performance in an underactuated system. Finally, numerical simulations are used to validate the effectiveness of the proposed control methodology.

Udwadia-Kalaba approach based distributed consensus control for multi-mobile robot systems with communication delays

In this paper, a distributed consensus algorithm for multi-mobile robot systems (MMRSs) with communication delays is proposed based on the Udwadia-Kalaba (UK) approach. The key feature of the proposed algorithm is that the consensus requirement is configured as a second-order constraint, and then a concise and explicit equation of motion for the constrained mechanical systems is formulated. Furthermore, the necessary and sufficient conditions for achieving the consensus of MMRSs with or without communication delays are developed under the network topology possessing a directed spanning tree. Finally, some numerical simulations are performed to verify the validity of the proposed consensus algorithm.

Optimal robust constraints-following control for rail vehicle virtual coupling

This paper puts forward the robust control problem of rail vehicle virtual coupling platoon that is subject to nonlinear and time-varying uncertainties. The uncertainties are caused by external disturbances and parameter variations. To this end, this paper designs a robust controller based on the Udwadia-Kalaba (UK) equation. First, we introduce the concept of virtual coupling and establish the longitudinal dynamics model of the rail vehicle. In order to ensure the control objective of the virtual coupling process, the spatial constraint on position and bidirectional inequality constraints for the spacing error between the marshalling trains are established. After changing the bounded state into the unbounded state through the state transformation, the UK approach can be used. Then, the constraint-following robust controller design is based on the UK approach and Lyapunov stability theory. The controller can render the unbounded state eventual uniform boundedness and uniform ultimate boundedness, which also satisfies the spatial constraint and the bidirectional restriction for the spacing error. Moreover, an optimized design scheme for the tunable parameter of this controller is proposed, which minimizes the control cost and comprehensive index of system performance. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods.

Robust Iterative Feedback Tuning Control of a Permanent Magnet Synchronous Motor with Repetitive Constraints: A Udwadia–Kalaba Approach

Robust Iterative Feedback Tuning Control of a Permanent Magnet Synchronous Motor with Repetitive Constraints: A Udwadia–Kalaba Approach

Correction to: Synchronization control for networked mobile robot systems based on Udwadia-Kalaba approach

Correction to: Synchronization control for networked mobile robot systems based on Udwadia-Kalaba approach

Synchronization control for networked mobile robot systems based on Udwadia–Kalaba approach

This paper addresses the problem of synchronization control for networked multi-mobile robot systems from the perspective of analytical mechanics. By reformulating the task requirement as a constrained motion problem, a unified synchronization algorithm for networked multi-mobile robot systems with or without leaders is proposed in combination with algebraic graph theory and the Udwadia–Kalaba approach. With the proposed algorithm, the networked mobile robot system can achieve synchronization from arbitrary initial conditions for the leaderless case and realize accurate trajectory tracking with explicitly given reference trajectories for the leader-following case. Numerical simulations of a networked wheeled mobile robot system are performed under different network structures and various trajectory requirements to show the performance of the proposed control algorithm.

Udwadia-Kalaba Equation Based Adaptive Robust Control for Two-wheeled Inverted Pendulum System: Underactuation and Uncertainty

A new adaptive robust control method based on Udwadia-Kalaba(U-K) approach which can be applied to the underactuated system is designed and used to two-wheeled inverted pendulum system in this paper. We separate this typical underactuated system into two subsystems(forward subsystem and yaw subsystem), which are fully underactuated and actuated. For these different subsystems, we use different control methods. We apply an adaptive robust control method which has been proved many times to the fully actuated subsystem. Based on this adaptive robust method, a new control strategy can be redesigned and applied to the underactuated subsystem by modifying the adaptive law and other things. This adaptive robust control with a leakage-type adaptive law could guarantee the uniform boundedness and uniform ultimate boundedness of the system. Finally, the simulation is executed to demonstrate the advantage and simplicity of the proposed method.

Constraint-force driven control design for rail vehicle virtual coupling

This study investigates the constraint-force driven control problem of virtual coupling. To solve the constraint force, the explicit equation of vehicle motion with equality constraints is established using the Udwadia–Kalaba approach. First of all, this study introduces a brief overview of virtual coupling concepts in the European Railway Traffic Management System and some scenes of virtual coupling. The control method is proposed to enable the mechanical system to follow the designed constraint. Moreover, the dynamic model for virtual coupling problem is established. Second, combined with the dynamic model, the equation constraint is designed to make the rail vehicle movenment reach the control objective. By solving the equation based on the Udwadia–Kalaba approach, the control inputs that can render the vehicle to move along the desired trajectory. Third, numerical simulation results demonstrate the effectiveness of the proposed method in virtual coupling problem.

Safety guaranteed longitudinal motion control for connected and autonomous vehicles in a lane‐changing scenario

This paper aims at utilising the ideology of controlling a constrained dynamical system to address the longitudinal motion control problem during lane-changing process subject to time-varying uncertainties. To this end, a robust controller is designed based on Udwadia–Kalaba (UK) approach and Lyapunov stability theory. Most of the studies on lane-changing considered only the equality constraint, namely the desired inter-vehicle distance. In a bilateral inequality constraint, the upper bound avoids unpredictable cut-ins and the lower bound collisions. This research applies the constraint to guarantee a safe and efficient lane-changing process. The original UK approach cannot handle bilateral inequalities. Therefore, a diffeomorphism method is proposed to transform the bounded state to an unbounded one. The latter enables the UK approach to deal with both equality and bilateral inequality constraints. The proposed controller can render each vehicle to adjust its distance with the predecessor without violating the prescribed bounds. Numerical experiments have been conducted to validate the effectiveness of the proposed controller under different traffic demands.

Embedding Robust Constraint-Following Control in Cooperative On-Ramp Merging

Cooperative on-ramp merging control for connected and automated vehicles have been widely studied in recent years. One of the major challenges for this multi-vehicle coordination problem is to execute a safe and efficient merging process considering realistic uncertainties in vehicle dynamics. This paper puts forward a two-layer merging control framework made up of centralized sequencing and distributed control. A Roadside Agent installed in the merging area identifies the merging sequence of vehicles approaching the merging area in terms of their estimated time of arrival at the merging point. Once the sequence is determined, distributed controllers will guide the vehicles to execute the merging process. The controller is designed based on Udwadia-Kalaba approach and Lyapunov stability theory and is capable of handling nonlinear vehicle dynamics and time-varying uncertainty. It renders both uniform boundedness and uniform ultimate boundedness performance for the spacing error and thus executes the merging process effectively. Simulations results verify the superiority of the proposed control method compared with baselines methods. Furthermore, the effectiveness of the proposed method is also validated under different traffic demands and multiple-vehicle-pack merging situation.