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Lane-deviation penalty formulation and analysis for autonomous vehicle avoidance maneuvers
Abstract
Autonomous vehicles hold promise for increased vehicle and traffic safety, and there are several developments in the field where one example is an avoidance maneuver. There it is dangerous for the vehicle to be in the opposing lane, but it is safe to drive in the original lane again after the obstacle. To capture this basic observation, a lane-deviation penalty (LDP) objective function is devised. Based on this objective function, a formulation is developed utilizing optimal all-wheel braking and steering at the limit of road–tire friction. This method is evaluated for a double lane-change scenario by computing the resulting behavior for several interesting cases, where parameters of the emergency situation such as the initial speed of the vehicle and the size and placement of the obstacle are varied, and it performs well. A comparison with maneuvers obtained by minimum-time and other lateral-penalty objective functions shows that the use of the considered penalty function decreases the time that the vehicle spends in the opposing lane.
... the lane-deviation penalty (LDP) function from (Anistratov et al., 2018a), penalizing deviations from the own driving lane of the vehicle, is transformed to the road-coordinate formulation H(n(s)) = H nr no (n(s)), (19) using the parameters n o and n r . ...
... The road right-hand side N r (s) is defined, adapting the approach in (Anistratov et al., 2018a), using (18) by N r (s(t)) = N r,1 ( H sr sou (s(t)) − H sr s od (s(t))) + N r,2 , (36) where the parameters of the function are set to: N r,1 = 2.5 m, N r,2 = −0.7 m, s r = 2 m, s ou = 23.5 m, s od = 36.5 m. The function (36) is illustrated with the bottom red line in Fig. 3. ...
Segmenting a motion-planning problem into smaller subproblems could be beneficial in terms of computational complexity. This observation is used as a basis for a new sub-maneuver decomposition approach investigated in this paper in the context of optimal evasive maneuvers for autonomous ground vehicles. The recently published alternating augmented Lagrangian method is adopted and leveraged on, which turns out to fit the problem formulation with several attractive properties of the solution procedure. The decomposition is based on moving the coupling constraints between the sub-maneuvers into a separate coordination problem, which is possible to solve analytically. The remaining constraints and the objective function are decomposed into subproblems, one for each segment, which means that parallel computation is possible and beneficial. The method is implemented and evaluated in a safety-critical double lane-change scenario. By using the solution of a low-complexity initialization problem and applying warm-start techniques in the optimization, a solution is possible to obtain after just a few alternating iterations using the developed approach. The resulting computational time is lower than solving one optimization problem for the full maneuver.
... The method is illustrated for a double lanechange maneuver, which is divided into three segments, although the method can be extended to any number of segments. The original problem from (Anistratov et al., 2018a) is modified to allow splitting into segments and the dual problem is subsequently formulated for parallel computation. Figure 1 shows a possible path for an example maneuver for the original problem. ...
A method to decompose a motion-planning problem into several segments is presented. It is based on a modification of the original problem, such that certain variables at the splitting points are considered to be precomputed and thus fixed and the remaining variables are obtained by performing Lagrange relaxation. The resulting dual problem is split into several subproblems, allowing parallel computation. The method is formalized as a computational algorithm and evaluated in a safety critical double lane-change situation. The resulting maneuver has close-to-optimal behavior and, for certain initialization strategies, it is obtained in shorter computational time compared to computing the full maneuver in one step.
Real-time avoidance maneuvers have been developed using a force-centric perspective, where the founding principles are obtained from studies of optimal maneuvers. The developed optimization framework, the different criteria used, and the obtained solutions give insight into how to control the forces on the vehicle. A highlight in this presentation is the first algorithm not needing a tire-road friction estimate.
Trajectory deviation occasions over handling limits are very dangerous because the vehicle is prone to stability loss or secondary collision owing to the large deviation. This article developed an optimal vehicle motion control algorithm in trajectory deviation occasions over handling limits for 4WIS-4WID vehicles. A double track 7DOF vehicle model and Magic Formula tire models are utilized to describe the vehicle dynamics. A quasi-projectile motion model is established considering Pontryagin minimum principle, based on which the trajectory deviation occasions recognition strategy and optimal control strategy and are developed. The effectiveness of the controller is verified through Matlab/Simulink. Simulation results show that the developed optimal control strategy can effectively decrease the maximum lateral error, in the meanwhile the computational complexity is much lower than the numerical nonlinear optimization. The control performance of the controller in 4WIS-4WID vehicles is better than 4WD and 2WS vehicles, proving the superiority of 4WIS-4WID vehicles.
The concept of utilizing vehicle-to-everything (V2X) connectivity to improve the resilience of automated vehicles in an environment where optical sensors may not provide reliable data is investigated. Longitudinal and lateral controllers are designed to enable a connected automated vehicle (CAV) to utilize V2X information from nearby connected human-driven vehicles (CHVs). The linear stability of the controllers are investigated theoretically while taking into account the time delays in the feedback loops. Novel performance measures are introduced to quantify the plant and string stability properties of the longitudinal controller from experimental data. The stability of the lateral controller is also evaluated in lane-keeping experiments. The robustness of the designed controllers against latency is demonstrated and the performance of the overall systems is showcased experimentally using real vehicles on a test track.
Autonomous vehicles allow utilisation of new optimal driving approaches that increase vehicle safety by combining optimal all-wheel braking and steering even at the limit of tyre–road friction. One important case is an avoidance manoeuvre that, in previous research, for example, has been approached by different optimisation formulations. An avoidance manoeuvre is typically composed of an evasive phase avoiding an obstacle followed by a recovery phase where the vehicle returns to normal driving. Here, an analysis of the different aspects of the recovery phase is presented, and a subsequent formulation is developed in several steps based on theory and simulation of a double lane-change scenario. Each step leads to an extension of the optimisation criterion. Two key results are a theoretical redundancy analysis of wheel-torque distribution and the subsequent handling of it. The overall contribution is a general treatment of the recovery phase in an optimisation framework, and the method is successfully demonstrated for three different formulations: lane-deviation penalty, minimum time, and squared lateral-error norm.
Without a driver to fall back on, a fully self-driving car needs to be able to handle any situation it can encounter. With the perspective of future safety systems, this research studies autonomous maneuvering at the tire-road friction limit. In these situations, the dynamics is highly nonlinear, and the tire-road parameters are uncertain.
To gain insights into the optimal behavior of autonomous safety-critical maneuvers, they are analyzed using optimal control. Since analytical solutions of the studied optimal control problems are intractable, they are solved numerically. An optimization formulation reveals how the optimal behavior is influenced by the total amount of braking. By studying how the optimal trajectory relates to the attainable forces throughout a maneuver, it is found that maximizing the force in a certain direction is important. This is like the analytical solutions obtained for friction-limited particle models in earlier research, and it is shown to result in vehicle behavior close to the optimal also for a more complex model.
Based on the insights gained from the optimal behavior, controllers for autonomous safety maneuvers are developed. These controllers are based on using acceleration-vector references obtained from friction-limited particle models. Exploiting that the individual tire forces tend to be close to their friction limits, the desired tire slip angles are determined for a given acceleration-vector reference. This results in controllers capable of operating at the limit of friction at a low computational cost and reduces the number of vehicle parameters used. For straight-line braking, ABS can intervene to reduce the braking distance without prior information about the road friction. Inspired by this, a controller that uses the available actuation according to the least friction necessary to avoid a collision is developed, resulting in autonomous collision avoidance without any estimation of the tire–road friction.
Investigating time-optimal lane changes, it is found that a simple friction-limited particle model is insufficient to determine the desired acceleration vector, but including a jerk limit to account for the yaw dynamics is sufficient. To enable a tradeoff between braking and avoidance with a more general obstacle representation, the acceleration-vector reference is computed in a receding-horizon framework.
The controllers developed in this thesis show great promise with low computational cost and performance not far from that obtained offline by using numerical optimization when evaluated in high-fidelity simulation.
In this paper, we tackle the problem of trajectory planning and control of a vehicle under locally varying traction limitations, in the presence of suddenly appearing obstacles. We employ concepts from adaptive model predictive control for run-time adaptation of tire force constraints that are imposed by local traction conditions. To solve the resulting optimization problem for real-time control synthesis with such time varying constraints, we propose a novel numerical scheme based on Real Time Iteration Sequential Quadratic Programming (RTI- SQP), which we call Sampling Augmented Adaptive RTI (SAA-RTI). Sampling augmentation of conventional RTI-SQP provides additional feasible candidate trajectories for warm-starting the optimization procedure. Thus, the proposed SAA- RTI algorithm enables real time constraint adaptation and reduces sensitivity to local minima. Through extensive numerical simulations we demonstrate that our method increases the vehicle’s capacity to avoid accidents in scenarios with unanticipated obstacles and locally varying traction, compared to equivalent non-adaptive control schemes and traditional planning and tracking approaches.
In order to safely navigate highly dynamic scenarios, automated vehicles must be able to react quickly to changes in the environment and be able to understand trade-offs between lateral and longitudinal forces when limited by tire-road friction. We present a design and experimental validation of a nonlinear model predictive controller that is capable of handling these complex situations. By carefully selecting the vehicle model and mathematical encodings of the vehicle and obstacles, we enable the controller to quickly compute inputs while maintaining an accurate model of the vehicle's motion and its proximity to obstacles. Experimental results of a test vehicle performing an emergency double lane change to avoid two ‛pop-up‚ obstacles demonstrate the ability of the controller to coordinate lateral and longitudinal tire forces even in emergency situations when the tires are at their friction limits.
Run-off-Road crashes are often associated with excessive speed in curves, which may happen when a driver is distracted or fails to compensate for reduced surface friction. This work introduces an Automated Emergency Cornering (AEC) system to protect against the major effects of over-speeding on curves, especially lateral deviation leading to lane or road departure. The AEC architecture has two levels: an upper level to perform motion planning, based on the optimal control of a nonlinear particle model, and a lower level to distribute the resulting two-dimensional acceleration reference to the available actuators. The lower level adopts the recently introduced Modified Hamiltonian Algorithm (MHA), which continuously adjusts the priority between mass-centre acceleration and yaw moment demands derived from lateral stability targets. AEC makes use of a high precision map and triggers control interventions based on vehicle kinematic states and detailed road geometry. To avoid false-positive interventions, AEC is triggered only when excessive road departure is predicted for the optimal particle motion. AEC then takes control of steering and individual wheel brake actuators to perform autonomous motion control for speed and path curvature at the limits of available friction. The AEC system is tested and evaluated using the high-fidelity simulation software CarMaker
With new developments in sensor technology, a new generation of vehicle dynamics controllers is developing, where the braking and steering strategies use more information, e.g. knowledge of road borders. The basis for vehicle-safety systems is how the forces from tyre–road interaction is vectored to achieve optimal total force and moment on the vehicle. To study this, the concept of attainable forces previously proposed in literature is adopted, and here a new visualisation technique is devised. It combines the novel concept of attainable force volumes with an interpretation of how the optimal solution develops within this volume. A specific finding is that for lane-keeping it is important to maximise the force in a certain direction, rather than to control the direction of the force vector, even though these two strategies are equivalent for the friction-limited particle model previously used in some literature for lane-keeping control design. More specifically, it is shown that the optimal behaviour develops on the boundary surface of the attainable force volume. Applied to lane-keeping control, this observation indicates a set of control principles similar to those analytically obtained for friction-limited particle models in earlier research, but result in vehicle behaviour close to the globally optimal solution also for more complex models and scenarios.
Stability control of a vehicle in autonomous safety-critical at-the-limit manoeuvres is analysed from the perspective of lane keeping or lane changing, rather than that of yaw control as in traditional ESC systems. An optimal control formulation is developed, where the optimisation criterion is a linear combination of the initial and final velocity of the manoeuvre. Varying the interpolation parameter in this formulation turns out to result in an interesting family of optimal braking and steering patterns in stabilising manoeuvres. The two different strategies of optimal lane-keeping control and optimal yaw control are shown to be embedded in the formulation and result from the boundary values of the parameter. The results provide new insights and have the potential to be used for future safety systems that adapt the level of braking to the situation at hand, which is demonstrated through examples of how to exploit theresults.
Development and deployment of steering based collision avoidance systems are made difficult due to the complexity of dealing with oncoming vehicles during the evasive manoeuvre. A method to mitigate the collision risk with oncoming vehicles during such manoeuvres is presented in this work. A point mass analysis of such a scenario is first done to determine the importance of speed for mitigating the collision risk with the oncoming vehicle. A characteristic parameter was identified, which correlates well with the need to increase or decrease speed, in order to reduce the collision risk. This finding was then verified in experiments using a Volvo XC90 test vehicle. A closed-loop longitudinal acceleration controller for collision mitigation with oncoming vehicles is then presented. The longitudinal control is combined with yaw stability control using control allocation to form an integrated controller. Simulations in CarMaker using a validated XC90 vehicle model and the proposed controller showed consistent reductions in the collision risk with the oncoming vehicle.
Lane change operation is widely used in numerous traffic scenarios; to minimize lane change time and avoid collisions with other vehicles required by intelligent vehicles, an optimal lane change motion is proposed for the shortest time free lane change and emergency obstacle avoidance lane change. First, two optimal lane change motion models are constructed based on a 3-degree-of-freedom dynamical vehicle model. Because of uncertain parameters in the vehicle model, the optimal lane change motion problem is an uncertain optimal control problem. Subsequently, targeted at nonlinearity and uncertain parameters, an extended adaptive pseudo-spectral method is also presented on the basis of approximate and numerical integration of parameter space. Finally, solving the optimal lane change motion problem, optimization results, control results based on the nonlinear model predictive control algorithm, and experimental results are shown under circumstances of certain vehicle mass and uncertain vehicle mass. As for uncertain parameters, optimization results are featured with robustness. Thus, uncertain parameters need not be measured, and optimization calculation need not be carried out in real time. The algorithm put forward here could be adopted to solve an uncertain optimal control problem. The optimal lane change motion can be extended to apply in more complex operations like merging, double-lane change, entering/exiting highways, or overtaking another vehicle.
A path planning and tracking framework is presented in order to maintain a collision free path for autonomous vehicles. For path planning approaches, a 3D virtual dangerous potential field is constructed as a superposition of trigonometric functions of the road and the exponential function of obstacles, which can generate a desired trajectory for collision avoidance when a vehicle collision with obstacles is likely to happen. Next, in order to track the planned trajectory for collision avoidance maneuvers, the path tracking controller formulates the tracking task as a Multi-constrained Model Predictive Control (MMPC) problem, and calculated the front steering angle to prevent the vehicle from colliding with a moving obstacle vehicle. Simulink and CarSim simulations are conducted in the case where moving obstacles exist. The simulation results show that the proposed path planning approach is effective for many driving scenarios and the MMPC-based path-tracking controller provides dynamic tracking performance and maintains good maneuverability.
There is currently a strongly growing interest in obtaining optimal control solutions for vehicle manoeuvres, both in order to understand optimal vehicle behaviour and, perhaps more importantly, to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is non-trivial to find the right combination of models, optimisation criteria, and optimisation tools to get useful results for the above purposes. Here, a platform for investigation of these aspects is developed based on a state-of-the-art optimisation tool together with adoption of existing vehicle chassis and tyre models. A minimum-time optimisation criterion is chosen for the purpose of gaining an insight into at-the-limit manoeuvres, with the overall aim of finding improved fundamental principles for future active safety systems. The proposed method to trajectory generation is evaluated in time-manoeuvres using vehicle models established in the literature. We determine the optimal control solutions for three manoeuvres using tyre and chassis models of different complexities. The results are extensively analysed and discussed. Our main conclusion is that the tyre model has a fundamental influence on the resulting control inputs. Also, for some combinations of chassis and tyre models, inherently different behaviour is obtained. However, certain variables important in vehicle safety-systems, such as the yaw moment and the body-slip angle, are similar for several of the considered model configurations in aggressive manoeuvring situations.
This paper addresses the issue of collision avoidance using lane-change maneuvers. Of particular interest is to determine the minimum distance beyond which an obstacle cannot be avoided at a given initial speed. Using a planar bicycle model, we first computer the sharpest dynamically feasible maneuver by minimizing the longitudinal distance of a lane transition, assuming given initial and free final speeds. The minimum distance to an obstacle is then determined from the path traced by the optimal maneuver. Plotting the minimum distance in the phase plane establishes the clearance curve, a valuable tool for planning emergency maneuvers. For the bicycle model, the clearance curve is shown to closely correlate with the straight line produced by a point mass model. Examples demonstrate the use of the clearance curve for planning safe avoidance maneuvers.
We present a dynamic stability and agility study of a pendulum-turn vehicle maneuver. Instead of optimizing the controlled inputs to mimic expert human driver performance, we focus on understanding the stability and agility performance of the vehicle motion using professional racing car driver testing data. We propose to use the rear side slip angle, rather than the vehicle mass center side slip angle, as one state variable to obtain the precise stable region. A hybrid physical/dynamic tire/road friction model is used to capture the dynamic friction force characteristics. We also introduce the use of vehicle lateral jerk and acceleration information as the agility metrics to compare maneuvering performance under the racing car driver and a typical human driver. The analysis and testing results show that during the pendulum-turn maneuvers, the professional driver operates the vehicle outside the stable regions of the vehicle dynamics to achieve superior agility performance than that under typical human driver control. Comparison results also show that the racing car driver outperforms in both the traveling time and the agility metrics. It is ongoing work to design a control strategy for autonomous aggressive maneuvers by using the new stability and agility results presented in this paper.
Active safety control is significant for ensuring the safety of both passengers and vehicles, and has been developed into various independent systems, such as anti-lock braking system, electronic stability programme system, steering by wire system, etc. However, with these independent systems, the control targets could intervene with each other. As a feasible strategy, the coordinated control, also namely the bottom-to-top control scheme, can improve the overall vehicle performance to some extent, but the performance compromises among independent controllers and the redundancies of sensor harness limit their full function display. In order to reach the maximum performance improvement, the top-to-bottom integrated motion control scheme for 4-wheel-independent vehicles considering critical conditions is developed in this paper, that is, the vehicle motion is controlled with a virtual control input on a top level, and then, the virtual control input is optimally allocated to and implemented by each wheel at the bottom level. The complicated allocation problem is handled via choosing proper allocation variables and corresponding allocation constraints, and meanwhile, the critical working conditions that could be created by emergency obstacle avoidance, cornering braking manoeuvre, etc., are considered to guarantee the vehicle stability. The effectiveness of the proposed controller is verified via simulations with different driving conditions.
Autonomous vehicle functions in safety-critical situations show promise in reducing the risk and saving lives in accidents compared to existing safety systems. Consequently, it is from many perspectives advantageous to be able to quantify the potential benefits of new autonomous systems for vehicle maneuvers at-the-limit of tire friction. Here, to estimate the potential in terms of saved lives and reduced degree of injuries in accidents for new, not yet existing systems, a framework has been developed by combining available historic data, in the form of crash databases, and statistical methods with comparative calculations of vehicle behavior using numerical optimization rather than simulation. The framework performs effectively, it gives interesting insights into the relation between more traditional active yaw control and optimal autonomous lane-keeping control, and it clearly demonstrates the potential of saved lives by using autonomous vehicle maneuvers.
We propose an adaptive nonlinear model predictive control (NMPC) for vehicle tracking control. The controller learns in real time a tyre force model to adapt to a varying road surface that is only indirectly observed from the effects of the tyre forces determining the vehicle dynamics. Learning the entire tyre model from data would require driving in the unstable region of the vehicle dynamics with a prediction model that has not yet converged. Instead, our approach combines NMPC with a noise-adaptive particle filter for vehicle state and tyre stiffness estimation and a pre-determined library of tyre models. The stiffness estimator determines the linear component of the tyre model during normal vehicle driving, and the control strategy exploits a relation between the tyre stiffness and the nonlinear part of the tyre force to select the appropriate full tyre model from the library, which is then used in the NMPC prediction model. We validate the approach in simulation using real vehicle parameters, demonstrate the real-time feasibility in automotive-grade processors using a rapid prototyping unit, and report preliminary results of experimental validation on a snow-covered test track.
In emergency situations, autonomous vehicles will be forced to operate at their friction limits in order to avoid collisions. In these scenarios, coordinating the planning of the vehicle's path and speed gives the vehicle the best chance of avoiding an obstacle. Fast reaction time is also important in an emergency, but approaches to the trajectory planning problem based on nonlinear optimization are computationally expensive. This paper presents a new scheme that simultaneously modifies the desired path and speed profile for a vehicle in response to the appearance of an obstacle, significant tracking error, or other environmental change. By formulating the trajectory optimization problem as a quadratically constrained quadratic program, solution times of less than 20 milliseconds are possible even with a 10 second planning horizon. A simplified point mass model is used to describe the vehicle's motion, but the incorporation of longitudinal weight transfer and road topography mean that the vehicle's acceleration limits are modeled more accurately than in comparable approaches. Experimental data from on an autonomous vehicle in two scenarios demonstrate how the trajectory planner enables the vehicle to avoid an obstacle even when the obstacle appears suddenly and the vehicle is already operating near the friction limits.
This paper considers the problem of collision avoidance for road vehicles, operating at the limits of friction. A two-level modelling and control methodology is proposed, with the upper level using a friction-limited particle model for motion planning, and the lower level using a nonlinear 3DOF model for optimal control allocation. Motion planning adopts a two-phase approach: the first phase is to avoid the obstacle, the second is to recover lane keeping with minimal additional lateral deviation. This methodology differs from the more standard approach of path-planning/path-following, as there is no explicit path reference used; the control reference is a target acceleration vector which simultaneously induces changes in direction and speed. The lower level control distributes vehicle targets to the brake and steer actuators via a new and efficient method, the Modified Hamiltonian Algorithm (MHA). MHA balances CG acceleration targets with yaw moment tracking to preserve lateral stability. A nonlinear 7DOF two-track vehicle model confirms the overall validity of this novel methodology for collision avoidance.
Lane change maneuver of high-speed automated vehicles is complicated since it involves highly nonlinear vehicle dynamics, which is critical for the driving safety and handling stability. Addressing this challenge, we present the dynamic modeling and control of high-speed automated vehicles for lane change maneuver. A nonlinear single-track vehicle dynamics model and a multi-segment lane change process model are employed. Variable time-steps are utilized for the vehicle model discretization to ensure a long enough prediction horizon while maintaining model fidelity and computational feasibility. Accordingly, the control of lane change maneuver is addressed in two successive stages. First, by considering the lane change maneuver as primarily a longitudinal control problem, velocity profiles are determined to ensure the longitudinal safety of this maneuver. Then, the associated lateral control is generated with a model predictive controller, taking the handling stability envelope, coupled tire forces and environmental constraints into account. Simulations demonstrate the real-time ability and stable-handling capability of the proposed approach.
Emergency scenarios may necessitate autonomous vehicle maneuvers up to their handling limits in order to avoid collisions. In these scenarios, vehicle stabilization becomes important to ensure that the vehicle does not lose control. However, stabilization actions may conflict with those necessary for collision avoidance, potentially leading to a collision. This paper presents a new control structure that integrates path tracking, vehicle stabilization, and collision avoidance and mediates among these sometimes conflicting objectives by prioritizing collision avoidance. It can even temporarily violate vehicle stabilization criteria if needed to avoid a collision. The framework is implemented using model predictive and feedback controllers. Incorporating tire nonlinearities into the model allows the controller to use all of the vehicle's performance capability to meet the objectives. A prediction horizon comprised of variable length time steps integrates the different time scales associated with stabilization and collision avoidance. Experimental data from an autonomous vehicle demonstrate the controller safely driving at the vehicle's handling limits and avoiding an obstacle suddenly introduced in the middle of a turn.
We present a primal-dual interior-point algorithm with a lter line-search method for non- linear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the fea- sibility restoration phase for the lter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlin- ear programming.
This paper presents and utilizes an optimal-control based method for quantifying the maneuverability of actively-controlled passenger vehicles during emergency highway-speed situations. The research is motivated by the desire to better understand the performance benefits of additional actuated degrees of freedom when compared to a typical vehicle. Specifically, the performance benefits of front-steer vehicles are compared to front-and rear-steer vehicles. In both cases, the vehicle is assumed to be capable of applying independent accelerating/braking torques to the front and rear wheels. The emergency maneuvers considered are obstacle avoidance, barrier avoidance, lane changes, and recovery from an arbitrary state. Necessary conditions for optimality and optimal control laws are found for each case. Solutions are found using a lumped-parameter planar single-track vehicle model and nonlinear tire dynamics are assumed. Front-and rear-steering vehicles are shown to have better maneuver-ability during all emergency maneuvers. Based on the optimal vehicle trajectories, the benefits are quantified using appropriate performance indices.
Lanekeeping assistance has the potential to save thousands of lives every year by preventing accidental road departure. This paper presents experimental validation of a potential field lanekeeping assistance system with quantitative performance guarantees. The lanekeeping system is implemented on a 1997 Corvette modified for steer-by-wire capability. With no mechanical connection between the hand wheel and road wheels the lanekeeping system can add steering inputs independently from the driver. Implementation of the lanekeeping system uses a novel combination of a multi-antenna Global Positioning System(GPS) and precision road maps. Preliminary experimental data shows that this control scheme performs extremely well for driver assistance and closely matches simulation results, verifying previous theoretical guarantees for safety. These results also motivate future work which will focus on interaction with the driver.
This paper presents an approach to vehicle control based on the paradigm of artificial po-tential fields. Using this method, the dynamics of the vehicle are coupled with the environment in a manner that ensures that the system exhibits safe motion in the absence of driver inputs. The driver remains in control of the vehicle, however, with the control systems presenting a predictable and safe set of dynamics. With the control approach presented here, integration of various assistance systems is easily achieved through simple superposition of individual poten-tial and damping functions. A simple example of a combined lanekeeping and stability system demonstrates how this can be accomplished. Preliminary simulation results suggest that both safety and driveability are achievable with such a system, prompting further investigation.
Following on the popularity of dynamic simulation for process systems, dynamic optimization has been identified as an important task for key process applications. In this study, we present an improved algorithm for simultaneous strategies for dynamic optimization. This approach addresses two important issues for dynamic optimization. First, an improved nonlinear programming strategy is developed based on interior point methods. This approach incorporates a novel filter-based line search method as well as preconditioned conjugate gradient method for computing search directions for control variables. This leads to a significant gain in algorithmic performance. On a dynamic optimization case study, we show that nonlinear programs (NLPs) with over 800,000 variables can be solved in less than 67 CPU minutes. Second, we address the problem of moving finite elements through an extension of the interior point strategy. With this strategy we develop a reliable and efficient algorithm to adjust elements to track optimal control profile breakpoints and to ensure accurate state and control profiles. This is demonstrated on a dynamic optimization for two distillation columns. Finally, these algorithmic improvements allow us to consider a broader set of problem formulations that require dynamic optimization methods. These topics and future trends are outlined in the last section.
The Modelica language, targeted at modeling of complex physical systems, has gained increased attention during the last decade. Modelica is about to establish itself as a de facto standard in the modeling community with strong support both within academia and industry. While there are several tools, both commercial and free, supporting simulation of Modelica models few efforts have been made in the area of dynamic optimization of Modelica models. In this paper, an extension to the Modelica language, entitled Optimica, is reported. Optimica enables compact and intuitive formulations of optimization problems, static and dynamic, based on Modelica models. The paper also reports a novel Modelica-based open source project, JModelica.org, specifically targeted at dynamic optimization. JModelica.org supports the Optimica extension and offers an open platform based on established technologies, including Python, C, Java and XML. Examples are provided to demonstrate the capabilities of Optimica and JModelica.org.
This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators--intermediaries between sample mean and sample median--that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators.
Segmentation and merging of autonomous at-the-limit maneuvers for ground vehicles
- P Anistratov
- B Olofsson
- L Nielsen
Collision avoidance and stabilization for autonomous vehicles in emergency scenarios
- J Funke
- M Brown
- Erlien
- Sm
Lane departure-based penalty for autonomous avoidance maneuvers
- P Anistratov
- B Olofsson
- L Nielsen
Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints
- J Ji
- A Khajepour
- Melek
- Ww