Karl Berntorp

Models and methodology for optimal trajectory generation in safety-critical road–vehicle manoeuvres

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.

Models and methodology for optimal vehicle maneuvers applied to a hairpin turn

There is currently a strongly growing interest in obtaining optimal control solutions for vehicle maneuvers, both in order to understand optimal vehicle behavior and to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is nontrivial to find the right mix of models, formulations, and optimization tools to get useful results for the above purposes. Here, a platform is developed based on a state-of-the-art optimization tool together with adoption of existing vehicle models, where especially the tire models are in focus. A minimum-time formulation is chosen to the purpose of gaining insight in at-the-limit maneuvers, with the overall aim of possibly finding improved principles for future active safety systems. We present optimal maneuvers for different tire models with a common vehicle motion model, and the results are analyzed and discussed. Our main result is that a few-state single-track model combined with different tire models is able to replicate the behavior of experienced drivers. Further, we show that the different tire models give quantitatively different behavior in the optimal control of the vehicle in the maneuver.

An Investigation of Optimal Vehicle Maneuvers for Different Road Conditions

We investigate optimal maneuvers for road-vehicles on different surfaces such as asphalt, snow, and ice. The study is motivated by the desire to find control strategies for improved future vehicle ...

Rao–Blackwellized Particle Filters With Out-of-Sequence Measurement Processing

This paper addresses the out-of-sequence measurement (OOSM) problem for mixed linear/nonlinear state-space models, which is a class of nonlinear models with a tractable, conditionally linear substructure. We develop two novel algorithms that utilize the linear substructure. The first algorithm effectively employs the Rao-Blackwellized particle filtering framework for updating with the OOSMs, and is based on storing only a subset of the particles and their weights over an arbitrary, predefined interval. The second algorithm adapts a backward simulation approach to update with the delayed (out-of-sequence) measurements, resulting in superior tracking performance. Extensive simulation studies show the efficacy of our approaches in terms of computation time and tracking performance. Both algorithms yield estimation improvements when compared with recent particle filter algorithms for OOSM processing; in the considered examples they achieve up to 10% enhancements in estimation accuracy. In some cases, the proposed algorithms even deliver accuracy that is similar to the lower performance bounds. Because the considered setup is common in various estimation scenarios, the developed algorithms enable improvements in different types of filtering applications.

Joint Wheel-Slip and Vehicle-Motion Estimation Based on Inertial, GPS, and Wheel-Speed Sensors

Joint wheel-slip and vehicle-motion estimation is considered, based on measurements from wheel encoders, an inertial measurement unit, and a global positioning system (GPS). The proposed strategy effectively employs the Rao-Blackwellized particle-filtering framework using a kinematic model. Key variables in active safety systems, such as longitudinal velocity, roll angle, and wheel slip for all four wheels, are estimated. The results from a demanding field test show the efficacy of the approach; the wheel slip and velocity can be estimated with an absolute accuracy of 0.018 and 0.25 m/s, respectively, measured as time-averaged root-mean-square errors, in periods of simultaneous aggressive braking and cornering. The corresponding differences between best case and worst case performances are 0.005 and 0.1 m/s. The results from a double lane-change maneuver indicate reliable velocity and slip estimation in periods of GPS outage.

Vehicle tracking control on piecewise-clothoidal trajectories by MPC with guaranteed error bounds

For control architectures of autonomous and semi-autonomous driving features, we design a vehicle steering controller with limited preview ensuring that the vehicle constraints are satisfied, and that any piecewise clothoidal trajectory, that is possibly generated by a path planner or supervisory algorithm and satisfies constraints on the desired yaw rate and the change of desired yaw rate, is tracked within a preassigned lateral error bound. The design is based on computing a non-maximal, yet polyhedral, robust control invariant (RCI) set for a system subject to bounded disturbances with state-dependent bounds, which also allows to determine the constraints describing the reference trajectories that can be followed. The RCI set is then enforced by model predictive control, where the cost function enforces additional objectives of the vehicle motion.

Hierarchical predictive control for ground-vehicle maneuvering

This paper presents a hierarchical approach to feedback-based trajectory generation for improved vehicle autonomy. Hierarchical vehicle-control structures have been used before-for example, in electronic stability control systems, where a low-level control loop tracks high-level references. Here, the control structure includes a nonlinear vehicle model already at the high level to generate optimization-based references. A nonlinear model-predictive control (MPC) formulation, combined with a linearized MPC acting as a backup controller, tracks these references by allocating torque and steer commands. With this structure the two control layers have a physical coupling, which makes it easier for the low-level loop to track the references. Simulation results show improved performance over an approach based on linearized MPC, as well as feasibility for online implementations.

Particle filter for combined wheel-slip and vehicle-motion estimation

The vehicle-estimation problem is approached by fusing measurements from wheel encoders, an inertial measurement unit, and (optionally) a global positioning system in a Rao-Blackwellized particle filter. In total 14 states are estimated, including key variables in active safety systems, such as longitudinal velocity, roll angle, and wheel slip for all four wheels. The method only relies on kinematic relationships. We present experimental data for one test scenario, using a Volkswagen Golf equipped with state-of-the-art sensors for determining ground truth. We report highly promising results, even for periods of combined aggressive cornering and braking.

Towards Lane-Keeping Electronic Stability Control for Road-Vehicles

The emerging new idea of lane-keeping electronic stability control is investigated. In a critical situation, such as entering a road curve at excessive speed, the optimal behavior may differ from the behavior of traditional ESC, for example, by prioritizing braking over steering response. The important question that naturally arises is if this has a significant effect on safety. The main contribution here is to give a method for some first quantitative measures of this. It is based on optimal control, applied to a double-track chassis model with wheel dynamics and high-fidelity tire-force modeling. The severity of accidents grows with the square of the kinetic energy for high velocities, so using kinetic energy as a measure will at least not overestimate the usefulness of the new safety system principle. The main result is that the safety gain is significant compared to traditional approaches based on yaw rotation, for several situations and different road-condition parameters.

Extending the Occupancy Grid Concept for Low-Cost Sensor Based SLAM

The simultaneous localization and mapping problem is approached by using an ultrasound sensor and wheel encoders. To be able to account for the low precision inherent in ultrasound sensors, the occupancy grid notion is extended. The extension takes into consideration with which angle the sensor is pointing, to compensate for the issue that an object is not necessarily detectable from all position due to deficiencies in how ultrasonic range sensors work. Also, a mixed linear/nonlinear model is derived for future use in Rao-Blackwellized particle smoothing.