A Tool for Lap Time Simulation

2007 Mediterranean Conference on Control &Amp; Automation

Lǚ

2007

In this work we initiate a mathematical analysis of rally racing techniques. An empirical description of Trail-Braking (TB) and Pendulum-Turn (PT) cornering, two of the most common rally racing maneuvers, is provided via analysis of data collected during execution of these maneuvers by an expert rally driver. Trail-Braking and Pendulum-Turn maneuvering techniques are reproduced using numerical optimization as special cases of the minimum time cornering problem with specific boundary conditions. We show that a simple parametrization of the control inputs can be used to reproduce these maneuvers using a high fidelity full-car model.

Section: Introductionmentioning

confidence: 99%

Aggressive maneuvers on loose surfaces: Data analysis and input parametrization

Velenis

2007 Mediterranean Conference on Control &Amp; Automation

Lǚ

2007

“…However, several complications arise from additional state and control constraints that make the problem more intricate than the standard time-optimal problem of the double-integrator [7]. Although "intuitive" solutions for this problem were known for sometime [8], [9], [10] (see also [11], [12], [13]), nonetheless, the work in [1], [3] was the first to offer a rigorous proof of optimality using optimal control theory. The necessary optimality conditions were explicitly derived, allowing one to determine the number and type of control switchings.…”

Section: Introductionmentioning

confidence: 99%

Optimal feedback velocity profile generation for a vehicle with given acceleration limits: A level set implementation

Jain

2008 16th Mediterranean Conference on Control and Automation

Velenis³

2008

In this paper, we use level set methods to numerically generate the minimum-time optimal velocity profiles for a vehicle with given acceleration limits driving along a specified path. The proposed approach solves the HamiltonJacobi-Bellman (HJB) equation associated with the given optimal control problem by computing the level sets of the value function. Once the optimal cost is found, the optimal feedback control can be computed online thus generating the velocity profile quickly. The results are compared to a semi-analytic approach that was developed recently for the same problem by the last two authors. I. INTRODUCTIONIn a series of recent papers the last two authors of this paper have developed a semi-analytic solution to the problem of optimal velocity generation of a point-mass vehicle on a prescribed path with a given, elliptical acceleration en-provides an alternative approach for the trajectory optimization problem of ground vehicles, which, typically, is dealt with in the literature using numerical methods [4], [5], [6]. These numerical optimization approaches are computationally intensive, and they cannot be readily applied in cases where the environment changes unpredictably. As a result, they are not suitable for real-time path-planning optimization. Motivated by the requirement to reduce the on-board computational cost, references [1], [2], [3] have exploited the potential of solving the trajectory planning problem (or at least part of this problem) analytically or semi-analytically. Indeed, for a point mass model moving on a given path, the problem is essentially one-dimensional (using the path arc length as the independent variable) with double-integrator dynamics. Hence, it can be readily solved. However, several complications arise from additional state and control constraints that make the problem more intricate than the standard time-optimal problem of the double-integrator [7]. Although "intuitive" solutions for this problem were known for sometime [8], [9], [10] (see also [11], [12], [13]), nonetheless, the work in [1], [3] was the first to offer a rigorous proof of optimality using optimal control theory. The necessary optimality conditions were explicitly derived, allowing one to determine the number and type of control switchings. In particular, the switching points can be found semi-analytically instead of numerically (as it was done in [11], [12] and [13]).

“…A point mass model of the vehicle is used, and the problem is formulated using an optimal control framework. A formal proof of the optimality of the semi-analytical method proposed in [6] and [7] to generate the optimal velocity profile is provided. Several problematic cases, in which loss of controllability occurs, and which were neglected in [6] and [7], are also discussed.…”

Section: Introductionmentioning

confidence: 99%

“…A formal proof of the optimality of the semi-analytical method proposed in [6] and [7] to generate the optimal velocity profile is provided. Several problematic cases, in which loss of controllability occurs, and which were neglected in [6] and [7], are also discussed. The methodology is of minimal computational cost, compared to common numerical optimization approaches, and is suitable for on-line implementation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal velocity profile generation for given acceleration limits: theoretical analysis

Velenis

Proceedings of the 2005, American Control Conference, 2005.

A semi-analytical method is proposed to generate minimum-time optimal velocity profiles for a vehicle with given acceleration limits driving along a specified path. The method is formally proven to provide optimal results using optimal control theory. In addition, several undesirable cases, where loss of controllability occurs, and which have been neglected in the literature, are being dealt with in this work.