Nonholonomic Kinematic Model Research Articles

Formation control of fixed-wing UAVs with communication delay

Fixed-wing unmanned aerial vehicles (UAVs) possess high speed and non-hovering capabilities, rendering them uniquely advantages for reconnaissance and detection. The focus of this paper is to addressing the problem of formation control for fixed-wing UAVs in the presence of communication delay. To tackle this problem, for the non-holonomic kinematic model, we propose an intuitive and practical control law based on the leader-follower method to ensure that UAVs maintain a predetermined geometric formation. The stability analysis of the system with communication delay is conducted by constructing a strict Lyapunov–Krasovskii function. Furthermore, we consider the impact of communication delay on formation accuracy and present a prediction algorithm capable of forecasting the actual position of each UAV. To validate our theoretical findings, both digital simulation and hardware-in-loop experiment are conducted.

Adaptive estimator‐based formation maneuvering control of nonholonomic mobile robots

SummaryIn this paper, the formation maneuvering control problem for a group of nonholonomic mobile robots with the objective of having a desired formation shape described by distances between pairs of robots and an overall maneuvering velocity is studied. The desired maneuvering velocity, which can be constant or time‐varying, is only known to a set of agents. A control scheme consisting of an adaptive estimator and a modified gradient control law is proposed to solve this problem. The adaptive estimator is designed to estimate the desired maneuvering velocity in either constant or time‐varying situation. Utilizing the estimated velocity, a modified gradient control law is designed based on the nonholonomic kinematic model so that the objective is achieved. Local asymptotic convergence of the overall system is guaranteed by choosing appropriate control parameters. The effectiveness of the proposed control scheme is demonstrated through simulation results.

On the Image Sensor Processing for Lane Detection and Control in Vehicle Lane Keeping Systems.

Lane keeping systems for a keeping a vehicle in the desired lane is key to advanced driving assistance system in autonomous vehicles. This paper presents a cost-effective image sensor with efficient processing algorithm for lane detection and lane control applications to autonomous delivery systems. The algorithm includes (1) lane detection by inverse perspective mapping and random sample consensus parabola fitting and (2) lane control by pure pursuit steering controller and classical proportional integral speed controller based on a nonholonomic kinematic model. The image sensor experiments conducted on a 1/10 scale model car maneuvering in a straight–curve–straight lane validate the better processing performance before, during, and after the turning section over previous work. The image sensor with the processing algorithm achieves the average lane detection error within 5% and maximum cross-track error within 9% in real-time. The development shall pave the way to cost-effective autonomous delivery systems.

Time-Varying Formation Tracking for Multiple UAVs with Nonholonomic Constraints and Input Quantization via Adaptive Backstepping Control

An adaptive control approach is presented for time-varying formation control of multiple UAVs with nonholonomic constraints and input quantization. The UAVs are described by nonholonomic kinematic model and autopilot model with uncertainties. A transverse function is designed to release the nonholonomic constraints. To avoid chattering, an enhanced hysteretic quantizer is utilized to process the input signals. The quantized signals are analyzed by a new decomposition method to release some restrictions. Based on Lyapunov stability theory, the adaptive backstepping controller is proposed for the formation tracking of multiple UAVs. Tuning functions are devised to make estimations of the unknown parameters and disturbances. A transformation function is applied to the control inputs to eliminate quantization effect. Stability analysis proves that the tracking errors can converge to the origin asymptotically, and all the signals in the closed-loop system are globally bounded. A simulation example is provided to illustrate the effectiveness of the proposed approach. Based on the control approach, the multi-UAV system can track the reference trajectory while forming and maintaining the predefined formation shape.

Adaptive finite‐time formation tracking control for multiple nonholonomic UAV system with uncertainties and quantized input

SummaryAn adaptive finite‐time formation tracking control approach is proposed for multiple unmanned aerial vehicle (UAV) system with quantized input signals in this paper. The UAVs are described by nonholonomic kinematic model and autopilot model with uncertainties. An enhanced hysteretic quantizer is introduced to avoid chattering, and some restrictions are released by using a new quantization decomposition method. Based on backstepping technique and finite‐time Lyapunov stability theory, the adaptive finite‐time controller is designed for the trajectory tracking of the multi‐UAV formation. The nonholonomic constraints are solved by a transverse function. A transformation is introduced to the control input signals to eliminate the quantization effect. Stability analysis proves that the tracking errors can converge to a small neighborhood of the origin within finite time and all the closed‐loop signals are semiglobally finite‐time bounded. The effectiveness of the proposed control approach is validated by simulation and experiment.

Adaptive Finite-Time Control for Formation Tracking of Multiple Nonholonomic Unmanned Aerial Vehicles with Quantized Input Signals

Signal quantization can reduce communication burden in multiple unmanned aerial vehicle (multi-UAV) system, whereas it brings control challenge to formation tracking of multi-UAV system. This study presents an adaptive finite-time control scheme for formation tracking of multi-UAV system with input quantization. The UAV model contains nonholonomic kinematic model and autopilot model with uncertainties. The nonholonomic states of the UAVs are transformed by a transverse function method. For input quantization, hysteretic quantizers are used to reduce the system chattering and new decomposition is introduced to analyze the quantized signals. Besides, a novel transformation of the control signals is designed to eliminate the quantization effect. Based on the backstepping technique and finite-time Lyapunov stability theory, the adaptive finite-time controller is established for formation tracking of the multi-UAV system. Stability analysis proves that the tracking error can converge to an adjustable small neighborhood of the origin within finite time and all the signals in closed-loop system are semiglobally finite-time bounded. Simulation experiment illustrates that the system can track the reference trajectory and maintain the desired formation shape.

Nonlinear Adaptive Output-Feedback Controller Design for Guidance of Flexible Needles

In this paper, a control methodology is proposed for guiding and stabilizing flexible bevel-tip needles to an arbitrary planar slice. The proposed controller is an adaptive version of the previously proposed nonlinear output feedback controller, which was built upon the well-known nonholonomic kinematic model of needle steering. On the grounds that such a model is subject to parametric uncertainty, an adaptive controller is necessary for adjusting the model parameters. In addition, a nonlinear observer is required due to the existence of some unmeasurable state variables. Although the original form of the studied system is linearly parameterized, its canonical form is not, preventing the application of conventional adaptive control schemes. In this paper, a nonlinear adaptive control methodology is proposed and applied to the guidance problem of steerable needles. Through simulation results, it is illustrated that the proposed methodology greatly outperforms the existing feedback linearization-based approach.

Extension of Model Predictive Static Programming for Reference Command Tracking

Reference command tracking control algorithm has been presented by extension of present Model Predictive Static Programming (MPSP) philosophy. The formulation uses nonlinear plant in discrete form and uses a cost function consisting of output tracking error and control deviations with corresponding weighing factors. The method finds the sensitivity matrices of output at each grid point of the trajectory, these sensitivity matrices can be computed recursively, making it computationally efficient. The control technique was applied to nonholonomic kinematic model of front wheel steered and driven three wheel mobile robot to track the commanded reference trajectory. Computational efficiency of present method makes it ideal for real time applications.

Coverage of curves in 3D with swarms of nonholonomic aerial robots

AbstractThis paper presents a vector field based methodology for coverage of curves in three-dimensional spaces with large groups of fixed-wing aerial robots. We model the robots as spheres with an associated nonholonomic kinematic model with minimum forward speed constraint. Under certain assumptions we guarantee that the robots will converge to and circulate along a desired curve avoiding inter-robot collisions while satisfying the constraints.

Rolling balls and octonions

In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain the geometric meaning of the basic invariants of vector distributions.

Image-guided Control of Flexible Bevel-Tip Needles.

Physicians perform percutaneous therapies in many diagnostic and therapeutic procedures. Image guidance promises to improve targeting accuracy and broaden the scope of needle interventions. In this paper, we consider the possibility of automating the guidance of a flexible bevel-tip needle as it is inserted into human tissue. We build upon a previously proposed nonholonomic kinematic model to develop a nonlinear observer-based controller. As a first step for control, we show that flexible needles can be automatically controlled to remain within a planar slice of tissue as they are inserted by a physician; our approach keeps the physician in the loop to control insertion speed. In the proposed controller, the distance of the needle tip position from the plane of interest is used as a feedback signal. Numerical simulations demonstrate the stability and robustness of the controller in the face of parametric uncertainty. We also present results from pilot physical experiments with phantom tissue under stereo image guidance.