Optimal planning and control for hazard avoidance of front-wheel steered ground vehicles

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 124-128).Hazard avoidance is an important capability for safe operation of robotic vehicles at high speed. It is also an important consideration for passenger vehicle safety, as thousands are killed each year in passenger vehicle accidents caused by driver error. Even when hazard locations are known, high-speed hazard avoidance presents challenges in real-time motion planning and control of nonlinear and potentially unstable vehicle dynamics. This thesis presents methods for planning and control of optimal hazard avoidance maneuvers for a bicycle model with front-wheel steering and wheel slip. The planning problem is posed as an optimization problem in which constrained dynamic quantities, such as friction circle utilization, are minimized, while ensuring a minimum clearance from hazards. These optimal trajectories can be computed numerically, though real-time computation requires simple models and constraints. To simplify the computation of optimal avoidance trajectories, analytical solutions to the optimal planning problem are presented for a point mass subject to an acceleration magnitude constraint, which is analogous to a tire friction circle constraint. The optimal point mass solutions are extended to a nonlinear bicycle model by defining a flatness-based trajectory tracking controller using tire force control. This controller decouples the bicycle dynamics into a point mass at the front center of oscillation with an additional degree of freedom related to the vehicle yaw dynamics. Structure is identified in the yaw dynamics and is exploited to characterize stability limits. Simulation results verify the stability properties of the yaw dynamics. These results were applied to a semi-autonomous driver assistance system and demonstrated experimentally on a full-sized passenger vehicle. Efficient computation of point mass avoidance maneuvers was used as a cost-to-go for real-time numerical optimization of trajectories for a bicycle model. The experimental system switches control authority between the driver and an automatic avoidance controller so that the driver retains control authority in benign situations, and the automatic controller avoids hazards automatically in hazardous situations.by Steven C. Peters.Ph.D

Novel piecewise trajectory shaping in Hill's canonical variables

Shape-based methods have been proven to be computationally efficient techniques to quickly estimate the cost of low-thrust interplanetary trajectories. However, in some cases the solution is far from optimal, like in the case of the exponential sinusoid, or requires a special treatment when the motion is not completely planar. More recent developments allows for a full three-dimensional representation of the trajectory but either constraints need to be imposed on the thrust direction or approximations need to be introduced on the trajectory time-evolution, causing the domain of representable trajectories to shrink. As a consequence, trajectories transferring to highly inclined or highly eccentric orbits can lead to infeasible control laws. This paper presents a new analytical framework for the quick estimation of the $\Delta v$ and peak thrust of two-point boundary value low-thrust transfers. The novelty of this method is that it solves an inverse optimal control problem in Hill's canonical variables. The parameterisation in Hill's variables was selected so that the shaping of the in-plane and out-of-plane motions can be treated separately and the boundary conditions can be analytically satisfied. This choice leads to a computationally efficient extraction of the control profile and allows for the integration of known analytical solutions for the in-plane motion. The computation of the value of the objective function (usually the total $\Delta v$ or the spacecraft final mass) and path constraints is reduced to computationally inexpensive quadratures. The shaping proposed in this paper is piecewise continuous and allows for a flexible full three-dimensional representation of the trajectory. In particular, the out-of-plane motion is represented by piecewise continuous functions so that one can independently maximise both the change of inclination and the variation of the longitude of the ascending node. The method is applied to some well-known test cases, a rendezvous with Mars, asteroid 1989ML and comet Tempel-1, and the results compared to the solutions obtained with exponential sinusoid, pseudoequinoctial elements and spherical shaping

Novel piecewise trajectory shaping in Hill's canonical variables

Shape-based methods have been proven to be computationally efficient techniques to quickly estimate the cost of low-thrust interplanetary trajectories. However, in some cases the solution is far from optimal, like in the case of the exponential sinusoid, or requires a special treatment when the motion is not completely planar. More recent developments allows for a full three-dimensional representation of the trajectory but either constraints need to be imposed on the thrust direction or approximations need to be introduced on the trajectory time-evolution, causing the domain of representable trajectories to shrink. As a consequence, trajectories transferring to highly inclined or highly eccentric orbits can lead to infeasible control laws. This paper presents a new analytical framework for the quick estimation of the $\Delta v$ and peak thrust of two-point boundary value low-thrust transfers. The novelty of this method is that it solves an inverse optimal control problem in Hill's canonical variables. The parameterisation in Hill's variables was selected so that the shaping of the in-plane and out-of-plane motions can be treated separately and the boundary conditions can be analytically satisfied. This choice leads to a computationally efficient extraction of the control profile and allows for the integration of known analytical solutions for the in-plane motion. The computation of the value of the objective function (usually the total $\Delta v$ or the spacecraft final mass) and path constraints is reduced to computationally inexpensive quadratures. The shaping proposed in this paper is piecewise continuous and allows for a flexible full three-dimensional representation of the trajectory. In particular, the out-of-plane motion is represented by piecewise continuous functions so that one can independently maximise both the change of inclination and the variation of the longitude of the ascending node. The method is applied to some well-known test cases, a rendezvous with Mars, asteroid 1989ML and comet Tempel-1, and the results compared to the solutions obtained with exponential sinusoid, pseudoequinoctial elements and spherical shaping

Search-based Motion Planning for Aggressive Flight in SE(3)

Quadrotors with large thrust-to-weight ratios are able to track aggressive trajectories with sharp turns and high accelerations. In this work, we develop a search-based trajectory planning approach that exploits the quadrotor maneuverability to generate sequences of motion primitives in cluttered environments. We model the quadrotor body as an ellipsoid and compute its flight attitude along trajectories in order to check for collisions against obstacles. The ellipsoid model allows the quadrotor to pass through gaps that are smaller than its diameter with non-zero pitch or roll angles. Without any prior information about the location of gaps and associated attitude constraints, our algorithm is able to find a safe and optimal trajectory that guides the robot to its goal as fast as possible. To accelerate planning, we first perform a lower dimensional search and use it as a heuristic to guide the generation of a final dynamically feasible trajectory. We analyze critical discretization parameters of motion primitive planning and demonstrate the feasibility of the generated trajectories in various simulations and real-world experiments.Comment: 8 pages, submitted to RAL and ICRA 201

A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects

Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal number of connected components based on attractive and repulsive pairwise terms. The two tasks are formulated on different levels of granularity and, accordingly, leverage mostly local information for motion segmentation and mostly high-level information for multi-target tracking. In this paper we argue that point trajectories and their local relationships can contribute to the high-level task of multi-target tracking and also argue that high-level cues from object detection and tracking are helpful to solve motion segmentation. We propose a joint graphical model for point trajectories and object detections whose Multicuts are solutions to motion segmentation {\it and} multi-target tracking problems at once. Results on the FBMS59 motion segmentation benchmark as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark demonstrate the promise of this joint approach