Spatio-temporal Motion Planning for Autonomous Vehicles with Trapezoidal Prism Corridors and B\'{e}zier Curves

Safety-guaranteed motion planning is critical for self-driving cars to generate collision-free trajectories. A layered motion planning approach with decoupled path and speed planning is widely used for this purpose. This approach is prone to be suboptimal in the presence of dynamic obstacles. Spatial-temporal approaches deal with path planning and speed planning simultaneously; however, the existing methods only support simple-shaped corridors like cuboids, which restrict the search space for optimization in complex scenarios. We propose to use trapezoidal prism-shaped corridors for optimization, which significantly enlarges the solution space compared to the existing cuboidal corridors-based method. Finally, a piecewise B\'{e}zier curve optimization is conducted in our proposed corridors. This formulation theoretically guarantees the safety of the continuous-time trajectory. We validate the efficiency and effectiveness of the proposed approach in numerical and CommonRoad simulations.Comment: Under Review at ACC 202

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

Trajectory generation for lane-change maneuver of autonomous vehicles

Lane-change maneuver is one of the most thoroughly investigated automatic driving operations that can be used by an autonomous self-driving vehicle as a primitive for performing more complex operations like merging, entering/exiting highways or overtaking another vehicle. This thesis focuses on two coherent problems that are associated with the trajectory generation for lane-change maneuvers of autonomous vehicles in a highway scenario: (i) an effective velocity estimation of neighboring vehicles under different road scenarios involving linear and curvilinear motion of the vehicles, and (ii) trajectory generation based on the estimated velocities of neighboring vehicles for safe operation of self-driving cars during lane-change maneuvers. ^ We first propose a two-stage, interactive-multiple-model-based estimator to perform multi-target tracking of neighboring vehicles in a lane-changing scenario. The first stage deals with an adaptive window based turn-rate estimation for tracking maneuvering target vehicles using Kalman filter. In the second stage, variable-structure models with updated estimated turn-rate are utilized to perform data association followed by velocity estimation. Based on the estimated velocities of neighboring vehicles, piecewise Bezier-curve-based methods that minimize the safety/collision risk involved and maximize the comfort ride have been developed for the generation of desired trajectory for lane-change maneuvers. The proposed velocity-estimation and trajectory-generation algorithms have been validated experimentally using Pioneer3- DX mobile robots in a simulated lane-change environment as well as validated by computer simulations

Real-Time Obstacle and Collision Avoidance System for Fixed-Wing Unmanned Aerial Systems

The motivation for the research presented in this dissertation is to provide a two-fold solution to the problem of non-cooperative reactive mid-air threat avoidance for fixed-wing unmanned aerial systems. The first phase is an offline UAS trajectory planning designed for an altitude-specific mission. The second phase leans on the results produced during the first phase to provide intelligent, real-time, reactive mid-air threat avoidance logic. That real-time operating logic provides a given fixed-wing UAS with local threat awareness so it can get a feel for the danger represented by a potential threat before using results produced during the first phase to require aircraft rerouting. The first original contribution of this research is the Advanced Mapping and Waypoint Generator (AMWG), a piece of software which processes publicly available elevation data in order to only retain the information necessary for a given altitude-specific flight mission. The AMWG is what makes systematic offline trajectory possible. The AMWG first creates altitude groups in order to discard elevations points which are not relevant to a specific mission because of the altitude flown at. Those groups referred to as altitude layers can in turn be reused if the original layer becomes unsafe for the altitude range in use, and the other layers are used for altitude re-scheduling in order to update the current altitude layer to a safer layer. Each layer is bounded by a lower and higher altitude, within which terrain contours are considered constant according to a conservative approach involving the principle of natural erosion. The AMWG then proceeds to obstacle contours extraction using threshold and edge detection vision algorithms. A simplification of those obstacle contours and their corresponding free space zones counterparts is performed using a fixed -tolerance Douglas-Peucker algorithm. This simplification allows free space zones to be described by vectors instead of point clouds, which enables UAS point location. The resulting geometry is then processed through a vertical trapezoidal decomposition where for each vertex defining a contour a vertical line is drawn, and the results of this decomposition is a set of trapezoidal cells. The cells corresponding to obstacle contours are then removed from the original trapezoidal decomposition in order to solely retain the obstacle-free trapezoidal cells. After decomposition, cells sharing part of a common edge are considered from a graph theory perspective so it becomes possible to list all acyclic paths between two cells by applying a depth first search (DFS) algorithm. The final product of the AWMG is a network of connected free space trapezoidal cells with embedded connectivity information referred to as the Synthetic Terrain Avoidance (STA network). The walls of the trapezoidal cells are then extruded as the AWMG essentially approximates a three-dimensional world by considering it as a stratification of two-dimensional layers, but the real-time phase needs 3D support. Using the graph conceptual view and the depth first search algorithm, all the connected cell sequences joining the departure to the arrival cell can be listed, a capability which is used during aircraft rerouting. By connecting two adjacent cells' centroids to their common midpoint located on the shared edge, the resulting flying legs remain within the two cells. The next step for paths between two cells is to be converted into flyable paths, and the conversion uses main and fallback methods to achieve that. The preferred method is the closed-form Dubins paths method involving the design of sequences of arc circle-straight line-arc circle (CLC) in order to account for the minimum radius turn constrain of the UAS. An additional geometric transformation is developed and applied to the initial waypoints used in the Dubins method so the flying leg directions are respected which is not possible by using the Dubins method alone. When consecutive waypoints are too close from one another, a condition called the Dubins condition cannot be respected, and the UAS trajectory design switches to the numerical integration of a system of ordinary differential equations accounting for the minimum turning constraint. Using the Dubins method and the ODE method makes it possible for the AWMG to design flyable offline trajectories accounting for the lateral dynamic of the fixed-wing UAS. The second original contribution of this research is the development and demonstration of the Double Dispersion reduction RRT (DDRRT), an algorithm which employs two new developed logic schemes respectively referred to as Punctual Dispersion Reduction (PDR), and Spatial Dispersion Reduction exploration (SDR). The DDRRT is employed during the real-time in-flight phase where it initially assumes a perfect terrain and no unpredictable threat, consequently following a 100% adaptive goal biasing toward the next waypoint in its list. When a threat such as an unpredicted obstacle is detected, the (PDR) acknowledges the fact that the DDRRT tree branches have met an obstacle and the its goal-biasing toward the next waypoint is decreased. If the PDR keeps decreasing, the DDRRT develops awareness of its surrounding obstacles by relaxing its PDR and switching to SDR which has the effect of increasing the dispersion of its branches, but keeping their extension bounded by the cell containing the last good position of the UAS, Csafe. If a number of branches reach a limit proportional to the Csafe and its relative area, then the STA network is queried for alternative rerouting. The two phases provide real-time reactive mid - air threat avoidance scenarios with the ability for a UAS to develop local and realistic threat awareness before considering intelligent rerouting. Either the local exploration of the DDRRT is successful before reaching a maximum number of points, or the STA Network is required to find another route

Optimal field coverage path planning on 2D and 3D surfaces

With the rapid adoption of automatic guidance systems, automated path planning has great potential to further optimize field operations. Field operations should be done in a manner that minimizes time, travel over field surfaces and is coordinated with specific field operations, machine characteristics and topographical features of arable lands. To reach this goal, intelligent coverage path planning algorithm is key. This dissertation documents our innovative research in optimal field coverage path planning on both 2D and 3D surfaces. To determine the full coverage pattern of a given 2D planar field by using boustrophedon paths, it is necessary to know whether to and how to decompose a field into sub-regions and how to determine the travel direction within each sub-region. A geometric model was developed to represent this coverage path planning problem, and a path planning algorithm was developed based on this geometric model. The search mechanism of the algorithm was guided by a customized cost function resulting from the analysis of different headland turning types and implemented with a divide-and-conquer strategy. The complexity of the algorithm was analyzed, and methods for reducing the computational time were discussed. Field examples with complexity ranging from a simple convex shape to an irregular polygonal shape that has multiple obstacles within its interior were tested with this algorithm. The results were compared with other reported approaches or farmers\u27 actual driving patterns. These results indicated the proposed algorithm was effective in producing optimal field decomposition and coverage path direction in each sub-region. In real world, a great proportion of farms have rolling terrains, which have considerable influences to the design of coverage paths. Coverage path planning in 3D space has a great potential to further optimize field operations. To design optimal coverage paths on 3D terrain surfaces, there were five important steps: terrain modeling and representation, topography impacts analysis, terrain decomposition and classification, coverage cost analysis and the development of optimal path searching algorithm. Each of the topics was investigated in this dissertation research. The developed algorithms and methods were successfully implemented in software and tested with practical 3D terrain farm fields with various topographical features. Each field was decomposed into sub-regions based on terrain features. An optimal seed curve was found for each sub-region and parallel coverage paths were generated by offsetting the seed curve sideways until the whole sub-region was completely covered. Compared with the 2D planning results, the experimental results of 3D coverage path planning showed its superiority in reducing both headland turning cost and soil erosion cost

Smooth path planning with Pythagorean-hodoghraph spline curves geometric design and motion control

This thesis addresses two significative problems regarding autonomous systems, namely path and trajectory planning. Path planning deals with finding a suitable path from a start to a goal position by exploiting a given representation of the environment. Trajectory planning schemes govern the motion along the path by generating appropriate reference (path) points. We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths that do not intersect with the obstacles of a given scenario. In the second step of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider Pythagorean\u2013hodograph (PH) curves, since they provide an exact computation of fundamental geometric quantities. The vertices of the previously produced piecewise linear paths are interpolated by using a G1 or G2 interpolation scheme with tension based on PH splines. In both cases, a strategy based on the asymptotic analysis of the interpolation scheme is developed in order to get an automatic selection of the tension parameters. To completely describe the motion along the path we present a configurable trajectory planning strategy for the offline definition of time-dependent C2 piece-wise quintic feedrates. When PH spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited

Static maritime enviroment representation of electronic navigational charts in global path planning

In past years, numerous global path planning methods have been researched and applied in maritime surface navigation. Regardless of intended usage for either decision-support in manned, or autonomous vessel navigation, path planning should generate a safe and efficient route. However, prior to route generation, static maritime environment representation must be created first. Whether it is transformed in to discrete or continuous form, common approach is to use Electronic Navigational Charts (ENCs) as a basis for maritime environment representation. Nevertheless its origins, ENCs still adhere to inherited data generalisations and simplifications to be comprehensible for human navigators. This leads to limitations when considering path planning and spatial resolution at different chart scales. Furthermore, when generating the representation and path, uncertainty must be considered since the quality and accuracy of chart data varies. Although these topics have been addressed separately in their respective domains, their relations have not been researched in detail. The aim of the proposed paper is the review of electronic navigational charts, environment representation and common global path planning approaches’ relations. Forthcoming standards and technologies, such as usage of high-density charts, are presented and discussed as well.Peer Reviewe

Optimal Coverage Path Planning for Arable Farming on 2D Surfaces

With the rapid adoption of automatic guidance systems in agriculture, automated path planning has great potential to further optimize field operations. Field operations should be done in a manner that minimizes time and travel over field surfaces and should be coordinated with specific field operation requirements, machine characteristics, and topographical features of arable lands. To reach this goal, an intelligent coverage path planning algorithm is the key. To determine the full coverage pattern of a given field by using boustrophedon paths, it is necessary to know whether to and how to decompose a field into sub-regions and how to determine the travel direction within each sub-region. A geometric model was developed to represent this coverage path planning problem, and a path planning algorithm was developed based on this geometric model. The search mechanism of the algorithm was guided by a customized cost function resulting from the analysis of different headland turning types and implemented with a divide-and-conquer strategy. The complexity of the algorithm was analyzed, and methods for reducing the computational time are discussed. Field examples with complexity ranging from a simple convex shape to an irregular polygonal shape that has multiple obstacles within its interior were tested with this algorithm. The results were compared with other reported approaches or farmers\u27 recorded patterns. These results indicate that the proposed algorithm was effective in producing optimal field decomposition and coverage path direction in each sub-region