Real-Time Collision Imminent Steering Using One-Level Nonlinear Model Predictive Control

Automotive active safety features are designed to complement or intervene a human driver's actions in safety critical situations. Existing active safety features, such as adaptive cruise control and lane keep assist, are able to exploit the ever growing sensor and computing capabilities of modern automobiles. An emerging feature, collision imminent steering, is designed to perform an evasive lane change to avoid collision if the vehicle believes collision cannot be avoided by braking alone. This is a challenging maneuver, as the expected highway setting is characterized by high speeds, narrow lane restrictions, and hard safety constraints. To perform such a maneuver, the vehicle may be required to operate at the nonlinear dynamics limits, necessitating advanced control strategies to enforce safety and drivability constraints. This dissertation presents a one-level nonlinear model predictive controller formulation to perform a collision imminent steering maneuver in a highway setting at high speeds, with direct consideration of safety criteria in the highway environment and the nonlinearities characteristic of such a potentially aggressive maneuver. The controller is cognizant of highway sizing constraints, vehicle handling capability and stability limits, and time latency when calculating the control action. In simulated testing, it is shown the controller can avoid collision by conducting a lane change in roughly half the distance required to avoid collision by braking alone. In preliminary vehicle testing, it is shown the control formulation is compatible with the existing perception pipeline, and prescribed control action can safely perform a lane change at low speed. Further, the controller must be suitable for real-time implementation and compatible with expected automotive control architecture. Collision imminent steering, and more broadly collision avoidance, control is a computationally challenging problem. At highway speeds, the required time for action is on the order of hundreds of milliseconds, requiring a control formulation capable of operating at tens of Hertz. To this extent, this dissertation investigates the computational expense of such a controller, and presents a framework for designing real-time compatible nonlinear model predictive controllers. Specifically, methods for numerically simulating the predicted vehicle response and response sensitivities are compared, their cross interaction with trajectory optimization strategy are considered, and the resulting mapping to a parallel computing hardware architecture is investigated. The framework systematically evaluates the underlying numerical optimization problem for bottlenecks, from which it provides alternative solutions strategies to achieve real-time performance. As applied to the baseline collision imminent steering controller, the procedure results in an approximate three order of magnitude reduction in compute wall time, supporting real-time performance and enabling preliminary testing on automotive grade hardware.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163063/1/jbwurts_1.pd

Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems

This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal control tools to problem classes where these tools have previously not been applicable. Today these problems are typically solved using motion planners based on randomized or graph search. The general principle is to define a homotopy that perturbs, or preferably relaxes, the original problem to an easily solved problem. By combining a Sequential Quadratic Programming (SQP) method with a homotopy approach that gradually transforms the problem from a relaxed one to the original one, practically relevant locally optimal solutions to the motion planning problem can be computed. The approach is demonstrated in motion planning problems in challenging 2D and 3D environments, where the presented method significantly outperforms a state-of-the-art open-source optimizing sampled-based planner commonly used as benchmark

Phase effects due to beam misalignment on diffraction gratings

All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent conditions for alignment stability. A framework for alignment stability with the use of diffractive elements was required using a Gaussian model. We successfully create such a framework involving modal decomposition to replicate small displacements of the beam (or grating) and show that the modal model does not contain the phase changes seen in an otherwise geometric planewave approach. The modal decomposition description is justified by verifying experimentally that the phase of a diffracted Gaussian beam is independent of the beam shape, achieved by comparing the phase change between a zero-order and first-order mode beam. To interpret our findings we employ a rigorous time-domain simulation to demonstrate that the phase changes resulting from a modal decomposition are correct, provided that the coordinate system which measures the phase is moved simultaneously with the effective beam displacement. This indeed corresponds to the phase change observed in the geometric planewave model. The change in the coordinate system does not instinctively occur within the analytical framework, and therefore requires either a manual change in the coordinate system or an addition of the geometric planewave phase factor.Comment: 14 pages, 8 figures, submitted to Optics Expres

Modeling flocks with perceptual agents from a dynamicist perspective

Computational simulations of flocks and crowds have typically been processed by a set of logic or syntactic rules. In recent decades, a new generation of systems has emerged from dynamicist approaches in which the agents and the environment are treated as a pair of dynamical systems coupled informationally and mechanically. Their spontaneous interactions allow them to achieve the desired behavior. The main proposition assumes that the agent does not need a full model or to make inferences before taking actions; rather, the information necessary for any action can be derived from the environment with simple computations and very little internal state. In this paper, we present a simulation framework in which the agents are endowed with a sensing device, an oscillator network as controller and actuators to interact with the environment. The perception device is designed as an optic array emulating the principles of the animal retina, which assimilates stimuli resembling optic flow to be captured from the environment. The controller modulates informational variables to action variables in a sensory-motor flow. Our approach is based on the Kuramoto model that describes mathematically a network of coupled phase oscillators and the use of evolutionary algorithms, which is proved to be capable of synthesizing minimal synchronization strategies based on the dynamical coupling between agents and environment. We carry out a comparative analysis with classical implementations taking into account several criteria. It is concluded that we should consider replacing the metaphor of symbolic information processing by that of sensory-motor coordination in problems of multi-agent organizations

Efficient calculation of sensor utility and sensor removal in wireless sensor networks for adaptive signal estimation and beamforming

Wireless sensor networks are often deployed over a large area of interest and therefore the quality of the sensor signals may vary significantly across the different sensors. In this case, it is useful to have a measure for the importance or the so-called "utility" of each sensor, e.g., for sensor subset selection, resource allocation or topology selection. In this paper, we consider the efficient calculation of sensor utility measures for four different signal estimation or beamforming algorithms in an adaptive context. We use the definition of sensor utility as the increase in cost (e.g., mean-squared error) when the sensor is removed from the estimation procedure. Since each possible sensor removal corresponds to a new estimation problem (involving less sensors), calculating the sensor utilities would require a continuous updating of different signal estimators (where is the number of sensors), increasing computational complexity and memory usage by a factor. However, we derive formulas to efficiently calculate all sensor utilities with hardly any increase in memory usage and computational complexity compared to the signal estimation algorithm already in place. When applied in adaptive signal estimation algorithms, this allows for on-line tracking of all the sensor utilities at almost no additional cost. Furthermore, we derive efficient formulas for sensor removal, i.e., for updating the signal estimator coefficients when a sensor is removed, e.g., due to a failure in the wireless link or when its utility is too low. We provide a complexity evaluation of the derived formulas, and demonstrate the significant reduction in computational complexity compared to straightforward implementations