Multi Vehicle Trajectory Planning On Road Networks

When multiple autonomous vehicles work in a shared space, such as in a surface mine or warehouse, they often travel along specified paths through a static road network. Although these vehicles’ actions and performance are coupled, their motion is often planned myopically or omits cooperation beyond avoiding collisions reactively. More desirable solutions could be achieved by coordinating and planning actions ahead of time. To make multi-vehicle systems more productive and efficient, the thesis introduces planning methods that can optimise for travel time, energy consumption, and trajectory smoothness. Vehicle motion is coordinated by using motion models that combine all trajectories, and avoid collisions. Mathematical programming is then used to find optimised solutions. The proposed methods are shown to significantly reduce solution costs compared to an approach based on common driving practices. As the number of vehicles and interactions between them increases, the number of solutions grows exponentially, making finding a solution computationally challenging. A major aim here was to find high quality solutions within practical computation times. To achieve this, techniques were developed that exploit the structure of the problems. This includes a heuristic algorithm that scales better with problem size, and is combined with the mathematical programming techniques to reduce their complexity. These were found to significantly reduce computation times, trading off marginal solution quality

Parallel Multi-Hypothesis Algorithm for Criticality Estimation in Traffic and Collision Avoidance

Due to the current developments towards autonomous driving and vehicle active safety, there is an increasing necessity for algorithms that are able to perform complex criticality predictions in real-time. Being able to process multi-object traffic scenarios aids the implementation of a variety of automotive applications such as driver assistance systems for collision prevention and mitigation as well as fall-back systems for autonomous vehicles. We present a fully model-based algorithm with a parallelizable architecture. The proposed algorithm can evaluate the criticality of complex, multi-modal (vehicles and pedestrians) traffic scenarios by simulating millions of trajectory combinations and detecting collisions between objects. The algorithm is able to estimate upcoming criticality at very early stages, demonstrating its potential for vehicle safety-systems and autonomous driving applications. An implementation on an embedded system in a test vehicle proves in a prototypical manner the compatibility of the algorithm with the hardware possibilities of modern cars. For a complex traffic scenario with 11 dynamic objects, more than 86 million pose combinations are evaluated in 21 ms on the GPU of a Drive PX~2

Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space