There is currently a strongly growing interest in obtaining optimal control solutions for vehicle maneuvers, both in order to understand optimal vehicle behavior 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 nontrivial to find the right combination of models, optimization criteria, and optimization 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 optimization tool together with adoption of existing vehicle chassis and tire models. A minimum-time optimization criterion is chosen to the purpose of gaining insight in at-the-limit maneuvers, with the overall aim of finding improved fundamental principles for future active safety systems. The proposed method to trajectory generation is evaluated in time-critical maneuvers using vehicle models established in literature. We determine the optimal control solutions for three maneuvers, using tire and chassis models of different complexity. The results are extensively analyzed and discussed. Our main conclusion is that the tire model has a fundamental influence on the resulting control inputs. Also, for some combinations of chassis and tire models, inherently different behavior 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 maneuvering situations.

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The problem of planning a trajectory for robots starting in an initial state and reaching a final state in a desired interval of time is tackled. We consider Model Predictive Control as an approach to the problem of point-topoint trajectory generation. We use the developed strategy to generate trajectories for transferring the state of the robot, fulfilling computational real-time requirements. Experiments on an industrial robot in a ball-catching scenario show the effectiveness of the approach. *The research leading to these results has received funding from the European Union's seventh framework program (FP7/2007-2013) under grant agreements PRACE (Ref. #285380

Abstract: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 safety and driver assistance technologies. Based on earlier presented measurements for tireforce characteristics, we develop tire models corresponding to different road conditions, and determine the time-optimal maneuver in a hairpin turn for each of these. The obtained results are discussed and compared for the different road characteristics. Our main findings are that there are fundamental differences in the control strategies on the considered surfaces, and that these differences can be captured with the adopted modeling approach. Moreover, the path of the vehicle center-of-mass was found to be similar for the different cases. We believe that these findings imply that there are observed vehicle behaviors in the results, which can be utilized for developing the vehicle safety systems of tomorrow.

Stability control of a vehicle in autonomous safety-critical at-thelimit 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 the results.

Abstract-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 stateof-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.

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