Kinematic Bicycle Model Research Articles

Local Path Planning for Nonholonomic Mobile Robots Based on Planar G2 Pythagorean Hodograph Degree 7 Bezier Transition Curves

The paper proposes a method that joins two line segments using planar Pythagorean hodograph (PH) degree 7 Bezier transition curves. The objective is to make use of such curvature-continuous curves for the path planning of nonholonomic constrained vehicles moving in 2D space, which requires designing a smooth path while satisfying the constraint of minimum turning radius. We initially present a novel idea that employs PH degree 7 Bezier transition curves for dealing with curvature constraints, the result of which proves to be better than the traditional method based on the “forward simulation”. The properties of PH degree 7 Bezier transition curves are then fully analyzed showing that the curves can be determined by a minimum of three parameters, each of which has an intuitive geometric meaning. The paper also proposes a path planner with direct curvature constraints during the process of path generation in 2D space. The objective function of the optimal path generation can be adjusted to minimize the length of the whole path or to closely follow the original global nonsmooth sequences of line segments. Here, the optimization problem is tactfully converted to a linear programming problem that can be solved efficiently. Finally, we use a kinematic bicycle model for simulation and compare the results with those from Dubins path showing that a [Formula: see text] curve is easier to follow than a [Formula: see text] one.

An Integrated Lateral and Longitudinal Decision-Making Model for Autonomous Driving Based on Deep Reinforcement Learning

Decision-making is an important component of autonomous driving perception, decision-making, planning, and control pipeline, which undertakes the task of how the ego vehicle makes high-level decision-making behaviors (such as lane change and car following) after sensing the environmental state, and then these high-level decision-making behaviors can be transmitted to the downstream planning and control module for specific low-level action execution. Based on the method of deep reinforcement learning (specifically, Deep Q network (DQN) and its variants), an integrated lateral and longitudinal decision-making model for autonomous driving is proposed in a multilane highway environment with both autonomous driving vehicle (ADV) and manual driving vehicle (MDV). The classic MOBIL and IDM models are used for the lateral and longitudinal decisions of MDV (i.e., lane changing and car following), while the lateral and longitudinal decisions of ADV are dominated by deep reinforcement learning models. In addition, this paper also uses the nonlinear kinematic bicycle model and two-point visual control model to realize the low-level control of both MDV and ADV. By setting a reasonable state, action, and reward function, this paper has carried out a large number of simulation experiments on the proposed autonomous driving decision-making model based on deep reinforcement learning in a three-lane road environment. The results show that under such scenario setting conditions, the deep reinforcement learning-based model proposed in this paper performs well in autonomous driving safety and travel efficiency. At the same time, when compared with the classical rule-based decision-making model (MOBIL&IDM), it is found that the model proposed in this paper can significantly achieve better results in episode rewards after stable training. In addition, through a large number of hyper-parameter tuning experiments, the performance of DQN, DDQN, and dueling DQN models, which are also deep reinforcement learning-based decision-making models, under different hyper-parametric configurations is compared and analyzed, which can provide a valuable reference for the specific scenario application of these models.

Stability analysis of a digital hierarchical steering controller of autonomous vehicles with multiple time delays

This study investigates the lane-keeping control of autonomous vehicles with an emphasis on the digital delayed nature of the system. The vehicle dynamics are represented using a kinematic bicycle model, and a hierarchical lane-keeping controller is introduced with multiple delays in the feedback loop. An extension of the semidiscretization method is presented, in order to perform the stability analysis of the digitally controlled vehicle with multiple discrete time delays. The differences between the continuous approximation and the exact consideration of discrete time delays are highlighted. We show that in certain cases, neglecting the effects of quantization can lead to significant inaccuracies, especially when tuning the lower-level controller. The results are verified using a series of small-scale laboratory experiments.

LQR ve Lyapunov temelli iki kontrolcünün kinematik bisiklet tipi model için güzergah izleme performansı karşılaştırması

This paper focuses on comparative results of two different controllers applied to kinematic bicycle model with rear wheel contact point to the ground as the reference point. The wide range of representation of different types of robots and vehicles of kinematic bicycle model is the main reason for this model selection. This paper has three main sections. The first section of the paper is mathematical modeling of the model. The second section is describing the utilized control techniques. The last section shares results of the simulations. The simulations have been carried out with pure feedback signals in absence of noise. The compared two controllers are an (Linear Quadratic Regulator)LQR controller and a Lyapunov based controller. The objective in the simulations is to track and complete a given constant radius trajectory. Last section includes comparison of results by analyzing statistical values of a defined error signal.

Modeling Driving Behavior of Human Drivers for Trajectory Planning

Extracted driving behavior of human driven vehicles can benefit the development of various applications like trajectory prediction or planning, abnormal driving detection, driving behavior classification, traffic simulation modeling, etc. In this paper, we focus on modeling human driving behavior in order to find simplifications for trajectory planning. Using a time-discrete kinematic bicycle model with the vehicle’s acceleration and steering rate as inputs, we model the human driven trajectories of an urban intersection drone dataset for different input sampling times. While most planning algorithms are using input sampling times below 0.33s, we are able to model 98.2% of the human driven trajectories of the investigated dataset with a sampling time of 0.6s. Using longer input sampling times can result in smoother trajectories and longer planning horizons, and thus more efficient trajectories. In a next step, we analyze the correlations between the input of our model and the current state/last input. Such a priori knowledge could simplify common planning algorithms like model predictive control or tree-search based planners by limiting the action space of the ego-vehicle. We propose nonlinear transformations for steering rate and steering angle to represent correlations between speed, acceleration, steering angle and steering rate. In the transformed space the statistics are very well modeled by multivariate Gaussian distributions. Using a multivariate Gaussian, a fast usable behavior model is extracted which is independent of the environment.

Optimal Control for Kinematic Bicycle Model With Continuous-Time Safety Guarantees: A Sequential Second-Order Cone Programming Approach

The optimal control problem for the kinematic bicycle model is considered where the trajectories are required to satisfy the safety constraints in the continuous-time sense. Based on the differential flatness property of the model, necessary and sufficient conditions in the flat space are provided to guarantee safety in the state space. The optimal control problem is relaxed to the problem of solving three second-order cone programs (SOCPs) sequentially, which find the safe path, the trajectory duration, and the speed profile, respectively. Solutions of the three SOCPs together provide a sub-optimal solution to the original optimal control problem. Simulation examples and comparisons with state-of-the-art optimal control solvers are presented to demonstrate the effectiveness of the proposed approach.

Time-Optimal Nonlinear Model Predictive Control for Radar-based Automated Parking

Motion planning and control are crucial components for automated vehicles. Especially in parking scenarios, high precision is required due to the small distances to obstacles. Common approaches utilize ultrasonic or camera sensors. This paper presents a radar-based system architecture for automated parking, which can operate more robustly under difficult weather conditions. Moreover, this work develops a unified planning and control framework based on nonlinear model predictive control. Real vehicles often exhibit dynamic behavior that the commonly used kinematic bicycle model does not represent. Therefore, the paper at hand proposes an extended model, which rests upon a systematic analysis of the test vehicle's dynamics for the low-velocity range. Experiments in simulation and on real-world data show the efficiency of the approach and the importance of the extended vehicle dynamics modeling for closed-loop control.

Autonomous Ground Vehicle Lane-Keeping LPV Model-Based Control: Dual-Rate State Estimation and Comparison of Different Real-Time Control Strategies.

In this contribution, we suggest two proposals to achieve fast, real-time lane-keeping control for Autonomous Ground Vehicles (AGVs). The goal of lane-keeping is to orient and keep the vehicle within a given reference path using the front wheel steering angle as the control action for a specific longitudinal velocity. While nonlinear models can describe the lateral dynamics of the vehicle in an accurate manner, they might lead to difficulties when computing some control laws such as Model Predictive Control (MPC) in real time. Therefore, our first proposal is to use a Linear Parameter Varying (LPV) model to describe the AGV’s lateral dynamics, as a trade-off between computational complexity and model accuracy. Additionally, AGV sensors typically work at different measurement acquisition frequencies so that Kalman Filters (KFs) are usually needed for sensor fusion. Our second proposal is to use a Dual-Rate Extended Kalman Filter (DREFKF) to alleviate the cost of updating the internal state of the filter. To check the validity of our proposals, an LPV model-based control strategy is compared in simulations over a circuit path to another reduced computational complexity control strategy, the Inverse Kinematic Bicycle model (IKIBI), in the presence of process and measurement Gaussian noise. The LPV-MPC controller is shown to provide a more accurate lane-keeping behavior than an IKIBI control strategy. Finally, it is seen that Dual-Rate Extended Kalman Filters (DREKFs) constitute an interesting tool for providing fast vehicle state estimation in an AGV lane-keeping application.

Scenario Analysis and Control Comparison for a High Speed Autonomous Vehicle

<div class="section abstract"><div class="htmlview paragraph">This paper studies the simulation and control of an autonomous dragster. Four scenarios are provided that are critical to vehicle and driver safety in drag racing. Equations are then created to model the behavior during these safety scenarios. The use of a kinematic bicycle model and a Newtonian wheel stand model are discussed for plane-of-motion and out-of-plane vehicle movement, respectively. A separate controller is designed for each model by comparing different control methods. Proportional-Integral-Derivative (PID) control, optimal control, and model predictive control (MPC) are presented and applied to the models. The models are simulated from a speed of 75 m/s, being the estimated top speed of the research vehicle, up to a top speed of 150.5 m/s which is in alignment with the highest recorded speed of a dragster. The comparison of the control techniques yields MPC as superior for the bicycle model and PID as sufficient for the wheel stand model. Latency of the system is also discussed and accounted for in the system.</div></div>

Model Predictive Trajectory Tracking for a Ground Vehicle in a Heterogeneous Rendezvous with a Fixed-Wing Aircraft

Abstract The maneuver of landing a fixed-wing unmanned aerial vehicle (UAV) autonomously on a moving ground platform requires precise spatial synchronization of both agents. Depending on the desired control strategy for the maneuver, the unmanned ground vehicle (UGV) must be capable to track the UAV’s trajectory robustly with respect to the ground plane even in the presence of disturbances such as wind gusts. In this paper, a linear model predictive trajectory tracking controller for a UGV based on a kinematic bicycle model is presented, assuming that the UAV aims at following a straight flight path with a given velocity. The vehicle model is discretized and linearized in each sampling step, resulting in a quadratic optimization problem which yields the optimal steering angle and motor current demand of the UGV. In the optimization problem, actuator constraints as well as hardware-related dead-times are taken into account. By constraining the yaw rate of the UGV, sideslip of the UGV is prevented, preserving the consistency of the kinematic model. Main requirements for the controller are the ability to allow sufficiently precise trajectory tracking with a longitudinal and lateral deviation of less than 0.5 m, i.e., within the dimensions of the landing platform in the given hardware setup, and real-time capability. Hardware-in-the-loop simulations and experimental results with a model-scale ground vehicle are presented that indicate the validity of the proposed control scheme.

Mechatronic design and implementation of a bicycle virtual reality system

The aim of this study is to design and implement a virtual reality bicycle system based on a functional-based mechatronic design approach. The development of virtual reality technologies with haptic systems demands a proper integration of the involved disciplines to provide immerse experiences for users. The proposed design approach provides a formal manner to gather the subsystems in the mechatronic device. The developed system is divided in a Virtual Reality System (VRS) and a Physical System (PS) for the design process. The former includes an interactive virtual environment in which an Avatar is animated using a simple kinematic bicycle model. The latter includes an adapted mountain bicycle with haptic feedback mechanisms to interact with the user and to produce the corresponding inputs for the bicycle model. Both systems are integrated by a control behavior system that works under two operation modes, where the user carries out virtual tours and gets feedbacks from a stereoscopic display system, audio cues, and haptic mechanisms. A multibody simulation validates the consistency and the integration of the physical system. In addition, a set of experimental results show the performance of instrumentation elements, control strategies, and feedback mechanisms, to provide the user with an immersive experience in the virtual environment. A brief survey was carried out to assess the opinion of users about the virtual bicycle tours, providing feedback for future improvements. The different designed modules and sub-systems allow modifying and enhancing the VRS without major modifications of the PS, or allow enhancing the physical platform without affecting the functionality of the virtual environment.

Event-Triggered 3D Needle Control Using a Reduced-Order Computationally Efficient Bicycle Model in a Constrained Optimization Framework

Long flexible needles used in percutaneous procedures such as biopsy and brachytherapy deflect during insertion, thus reducing needle tip placement accuracy. This paper presents a surgeon-in-the-loop system to automatically steer the needle during manual insertion and compensate for needle deflection using an event-triggered controller. A reduced-order kinematic bicycle model incorporating needle tip measurement data from ultrasound images is used to determine steering actions required to minimize needle deflection. To this end, an analytic solution to the reduced-order bicycle model, which is shown to be more computationally efficient than a discrete-step implementation of the same model, is derived and utilized for needle tip trajectory prediction. These needle tip trajectory predictions are used online to optimize the insertion depths (event-trigger points) for steering actions such that needle deflection is minimized. The use of the analytic model and the event-triggered controller also allows for limiting the number and extent of needle rotations (to reduce tissue trauma) in a constrained optimization framework. The system was tested experimentally in three different ex-vivo tissue phantoms with a surgeon-in-the-loop needle insertion device. The proposed needle steering controller was shown to keep the average needle deflection within 0.47 [Formula: see text] 0.21[Formula: see text]mm at the final insertion depth of 120[Formula: see text]mm.

Experimental Validation of a Kinematic Bicycle Model Predictive Control with Lateral Acceleration Consideration

Abstract Nowadays, Automated Driving has a growing interest in the scientific and industrial automotive community. The vehicle motion planning is an essential procedure to obtain safe and comfortable trajectories, adapting the longitudinal speed to the road legal limits and mainly to avoid the excessive lateral accelerations along the journey. Typically, the proper speed of the vehicle is intrinsically related to the curvature of the path, requiring a previous approximation of this parameter in the planning stage. In this work, a novel procedure to follow a route trajectory and speed limits considering the lateral acceleration parameter is presented. A lateral jerk equation was developed and introduced into a kinematic bicycle model predictive control formulation. An adaptive speed weight equation that depends on the lateral acceleration is presented to improve the lateral positioning. A vehicle motion control simulation, developed in Dynacar, is validated with some real tests. The results show the capabilities of the proposed approach. An accurate vehicle motion control considers the lateral acceleration to avoid unfeasibility in optimization problem.

Discussion on: “Adaptive and Predictive Path Tracking Control for Off-road Mobile Robots”

The authors are addressing the problem of accuratepath tracking in off-road terrains in presence oflateral sliding, with particular application to agri-culture vehicles. The adherence conditions are notmodeled explicitly (i.e. no tire to ground model),however the lateral sliding angles of the wheels areintegrated in the kinematic bicycle model, calledextended kinematic model. An observer is used toestimate the unknown sliding angles on-line withrespect to steady-state adherence conditions. A steer-ing wheel controller based on chained form trans-formation of the kinematic bicycle model for theparametric curve tracking is used. Furthermore, inorder to compensate for abrupt curvature changesand low level control delay, a model predictive con-trol signal is added. Experimental verification isprovided on slippery, wet ground for straight driv-ing on a slope and curved path driving on flat ground,with good tracking results achieved, close to setrequirements.