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

Fast and Safe Trajectory Optimization for Autonomous Mobile Robots using Reachability Analysis

Autonomous mobile robots (AMRs) can transform a wide variety of industries including transportation, shipping and goods delivery, and defense. AMRs must match or exceed human performance in metrics for task completion and safety. Motion plans for AMRs are generated by solving an optimization program where collision avoidance and the trajectory obeying a dynamic model of the robot are enforced as constraints. This dissertation focuses on three main challenges associated with trajectory planning. First, collision checks are typically performed at discrete time steps. Second, there can be a nontrivial gap between the planning model used and the actual system. Finally, there is inherent uncertainty in the motion of other agents or robots. This dissertation first proposes a receding-horizon planning methodology called Reachability-based Trajectory Design (RTD) to address the first and second challenges, where uncertainty is dealt with robustly. Sums-of-Squares (SOS) programming is used to represent the forward reachable set for a dynamic system plus uncertainty, over an interval of time, as a polynomial level set. The trajectory optimization is a polynomial optimization program over a space of trajectory parameters. Hardware demonstrations are implemented on a Segway, rover, and electric vehicle. In a simulation of 1,000 trials with static obstacles, RTD is compared to Rapidly-exploring Random Tree (RRT) and Nonlinear Model Predictive Control (NMPC) planners. RTD has success rates of 95.4% and 96.3% for the Segway and rover respectively, compared to 97.6% and 78.2% for RRT and 0% for NMPC planners. RTD is the only successful planner with no collisions. In 10 simulations with a CarSim model, RTD navigates a test track on all trials. In 1,000 simulations with random dynamic obstacles RTD has success rates of 96.8% and 100% respectively for the electric vehicle and Segway, compared to 77.3% and 92.4% for a State Lattice planner. In 100 simulations performing left turns, RTD has a success rate of 99% compared to 80% for an MPC controller tracking the lane centerline. The latter half of the dissertation treats uncertainty with the second and/or third challenges probabilistically. The Chance-constrained Parallel Bernstein Algorithm (CCPBA) allows one to solve the trajectory optimization program from RTD when obstacle states are given as probability functions. A comparison for an autonomous vehicle planning a lane change with one obstacle shows an MPC algorithm using Cantelli's inequality is unable to find a solution when the obstacle's predictions are generated with process noise three orders of magnitude less than CCPBA. In environments with 1-6 obstacles, CCPBA finds solutions in 1e-3 to 1.2 s compared to 1 to 16 s for an NMPC algorithm using the Chernoff bound. A hardware demonstration is implemented on the Segway. The final portion of the dissertation presents a chance-constrained NMPC method where uncertain components of the robot model are estimated online. The application is an autonomous vehicle with varying road surfaces. In the first study, the controller uses a linear tire force model. Over 200 trials of lane changes at 17 m/s, the chance-constrained controller has a cost 86% less than a controller using fixed coefficients for snow, and only 29% more than an oracle controller using the simulation model. The chance-constrained controller also has 0 lateral position constraint violations, while an adaptive-only controller has minor violations. The second study uses nonlinear tire models on a more aggressive maneuver and provides similar results.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169729/1/skvaskov_1.pd