Craig E. Beal

Model Predictive Control for Vehicle Stabilization at the Limits of Handling

Recent developments in vehicle steering systems offer new opportunities to measure the steering torque and reliably estimate the vehicle sideslip and the tire-road friction coefficient. This paper presents an approach to vehicle stabilization that leverages these estimates to define state boundaries that exclude unstable vehicle dynamics and utilizes a model predictive envelope controller to bound the vehicle motion within this stable region of the state space. This approach provides a large operating region accessible by the driver and smooth interventions at the stability boundaries. Experimental results obtained with a steer-by-wire vehicle and a proof of envelope invariance demonstrate the efficacy of the envelope controller in controlling the vehicle at the limits of handling.

Predictive control of vehicle roll dynamics with rear wheel steering

A pair of model predictive controllers (MPCs) capable of modifying the nominal roll dynamics of a vehicle through control of the planar vehicle dynamics are presented. Each of these controllers is based on a linear model of the vehicle. One controller utilizes differential drive of the rear axle to modify the planar motion, while the other uses rear-wheel-steering (RWS). Results from simulations of a nonlinear vehicle model executing maneuvers with each of the controllers demonstrate that the differential-drive technique results in significant lateral-longitudinal tire force coupling and saturation that degrades the validity of the internal model used for MPC. The RWS controller commands very small steering angles, retaining the validity of the model and showing better performance for the desired roll control task.

A Method for Incorporating Nonlinear Tire Behavior Into Model Predictive Control for Vehicle Stability

Given the increase in computing power over the last decade, model predictive control has received renewed attention as a technique for accomplishing high-level vehicle control. However, tire nonlinearities present a challenge for rapidly solving the optimization problem required to do model predictive control. This paper presents an approach which extracts the tire nonlinearities outside the MPC optimization, leaving a convex problem that can be solved rapidly and with guaranteed optimality. Experimental results are presented from an MPC controller using this technique that demonstrate the controller’s ability to handle tire nonlinearities during highly dynamic manuevers that saturate the tires and induce lateral-longitudinal force coupling effects.Copyright

Controlling Vehicle Instability Through Stable Handling Envelopes

Loss of control accidents result in thousands of fatalities in the United States each year. Production stability control systems are highly effective in preventing these accidents, despite their reliance on a hand-tuned response to data from a small set of sensors. However, improvements in sensing offer opportunities to determine stabilizing actions in a more systematic manner. This paper presents an approach that utilizes the yaw-sideslip phase plane to choose boundaries that eliminate unstable and undesirable driving regimes. These boundaries may be varied to obtain desirable performance and driver acceptance and form the basis for a driver assistance system that augments the driver input to maintain the vehicle within the bounds of a safe handling envelope. Experimental results from a model predictive controller used to enforce the envelope boundaries on a steer-by-wire vehicle are presented to demonstrate the viability of this framework for implementing stability boundaries.Copyright

Experimental Validation of a Linear Model Predictive Envelope Controller in the Presence of Vehicle Nonlinearities

Abstract As manufacturers offer glimpses of their future vehicles, it is apparent that computational power and sensory information will significantly increase. These advances offer the opportunity to design a controller that leverages new information to improve stability while attaining a higher level of coordination with the driver. In this paper, the authors present an approach that utilizes axle slip angles to define an envelope in which the vehicle behavior is stable and predictable. A linear model predictive controller using front active steering is developed. Experimental results using a steer-by-wire test vehicle are presented to demonstrate the functionality of the controller. Analysis of the results includes discussion of the limitations of the linear controller in controlling the vehicle at the limits of handling and how disturbances and unmodeled driver input can cause the slip angles to deviate from this envelope.

Enhancing Vehicle Stability Through Model Predictive Control

Vehicle stability control systems have been widely and accurately cited as a significant influence in reducing the rate of severe injuries and fatalities in automotive crashes. However, these systems are purely reactive, providing additional control input only after undesired vehicle behavior is sensed. This paper presents a new approach to controlling the motion of a vehicle in highly dynamic situations. This approach solves a convex optimization problem over a finite time horizon to predict and prevent these hazardous situations. Thus, the controller determines input that simultaneously tracks the driver’s intended trajectory while preventing tire saturation. Simulation results are presented to demonstrate the efficacy of this control approach.Copyright

Coupled lateral-longitudinal vehicle dynamics and control design with three-dimensional state portraits

ABSTRACT The dynamics of vehicles with pneumatic tyres are well-known to be non-holonomic, nonlinear, and subject to state bounds in order to remain on defined roadways. As such, it can be challenging to apply many of the tools typically used to analyse nonlinear dynamics and synthesise control strategies. Furthermore, the use of traditional stability analyses is often insufficient for vehicle control design since adherence to the roadway geometry implies a constrained space that dictates stricter conditions on the states than provable stability. A two-state phase portrait approach has been used to analyse vehicle dynamics and provides an illustrative view of the state trajectories at constant speed. This paper extends the phase portrait to three states to represent the nonlinear vehicle dynamics with steering and longitudinal tyre force inputs and consideration of the longitudinal vehicle dynamics. The concept of a fixed point in the phase plane is extended to a stable curve and example controllers are examined and synthesised using the three-dimensional vector space.

Vehicle control synthesis using phase portraits of planar dynamics

ABSTRACT Phase portraits provide control system designers strong graphical insight into nonlinear system dynamics. These plots readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and system inputs. This paper extends the usage of phase portraits in vehicle dynamics to control synthesis by illustrating the relationship between the boundaries of stable vehicle operation and the state derivative isoclines in the yaw rate–sideslip phase plane. Closed-loop phase portraits demonstrate the potential for augmenting a vehicles open-loop dynamics through steering and braking. The paper concludes by applying phase portrait analysis to an envelope control algorithm for yaw stability and a sliding surface controller for stabilising a saddle point equilibrium in drifting.

Vehicle Stabilization During Critical Cornering Scenarios Using Sliding Surface Control

While effective in improving handling and passenger safety, current vehicle control systems are generally limited to braking or steering control. This project presents an approach which integrates steering and braking actuation to further improve vehicle stability in critical cornering scenarios. A 3D phase portrait visualization tool enables examination of lateral velocity, longitudinal velocity, and yaw rate. This tool is used to determine vehicle stability under different operating conditions to inform the design of a controller. The proposed hierarchical controller defines a path-following function for the desired cornering radius and determines appropriate braking and steering inputs, using sliding surface control, to drive the vehicle to the desired path. A low-complexity vehicle model is used to formulate the sliding surface, while a high-fidelity model is used to determine optimal inputs. Simulations show that the sliding surface controller design is more effective than a baseline steering controller in keeping the vehicle on the roadway. Examination reveals that the complex sequence of braking and steering inputs is only feasible with the addition of a modern vehicle control system. While average drivers lack the ability to effectively employ such complex sequencing, modern control systems are capable of this coordination. When entering corners at speeds within the capability of the vehicle, but beyond the ability of the driver, these control sequences can help maintain stability to avoid an accident.

Stabilization of a vehicle traversing a short low-friction road segment

In normal vehicle operation, drivers occasionally encounter low friction patches without advance warning. The sudden transitions to and from the low friction surface may destabilize the vehicle, even when the operating point on the higher friction surface is away from the handling limits. Because of these fast dynamics, an active assistance system could significantly enhance safety. This paper describes the dynamics of transition between friction surfaces and demonstrates the utility of an envelope controller that uses real-time friction estimates and a state-bounding approach. Experimental data and the controller state bounds are used to provide insight into the trade-off between estimator accuracy and response time when used for real-time control.