On the performance of random linear projections for sampling-based motion planning

Sampling-based motion planners are often used to solve very high-dimensional planning problems. Many recent algorithms use projections of the state space to estimate properties such as coverage, as it is impractical to compute and store this information in the original space. Such estimates help motion planners determine the regions of space that merit further exploration. In general, the employed projections are user-defined, and to the authors’ knowledge, automatically computing them has not yet been investigated. In this work, the feasibility of offline-computed random linear projections is evaluated within the context of a state-of-the art sampling-based motion planning algorithm. For systems with moderate dimension, random linear projections seem to outperform human intuition. For more complex systems it is likely that non-linear projections would be better suited

Temporal Logic Motion Planning in Partially Unknown Environments

This thesis considers the problem of a robot with complex dynamics navigating a partially discovered environment to satisfy a temporal logic formula consisting of both a co-safety formula component and a safety formula component. We employ a multi-layered synergistic framework for planning motions to satisfy a temporal logic formula, and we combine with it an iterative replanning strategy to locally patch the robot's discretized internal representation of the workspace whenever a new obstacle is discovered. Furthermore, we introduce a notion of ``closeness'' of satisfaction of a linear temporal logic formula, defined by a metric over the states of the corresponding automaton. We employ this measure to maximize partial satisfaction of the co-safety component of the temporal logic formula when obstacles render it unsatisfiable. For the safety component of the specification, we do not allow partial satisfaction. This introduces a general division between ``soft'' and ``hard'' constraints in the temporal logic specification, a concept we illustrate in our discussion of future work. The novel contributions of this thesis include (1) the iterative replanning strategy, (2) the support for safety formulas in the temporal logic specification, (3) the method to locally patch the discretized workspace representation, and (4) support for partial satisfaction of unsatisfiable co-safety formulas. As our experimental results show, these methods allow us to quickly compute motion plans for robots with complex dynamics to satisfy rich temporal logic formulas in partially unknown environments

Investigating the impact of triangle and quadrangle mesh representations on AGV path planning for various indoor environments: With or without inflation

In a factory with different kinds of spatial atmosphere (warehouses, corridors, small or large workshops with varying sizes of obstacles and distribution patterns), the robot’s generated paths for navigation tasks mainly depend on the representation of that environment. Hence, finding the best representation for each particular environment is necessary to forge a compromise between length, safety, and complexity of path planning. This paper aims to scrutinize the impact of environment model representation on the performance of an automated guided vehicle (AGV). To do so, a multi-objective cost function, considering the length of the path, its complexity, and minimum distance to obstacles, is defined for a perfect circular robot. Unlike other similar studies, three types of representation, namely quadrangle, irregular triangle, and varying-size irregular triangle, are then utilized to model the environment while applying an inflation layer to the discretized view. Finally, a navigation scenario is tested for different cell decomposition methods and an inflation layer size. The obtained results indicate that a nearly constant coarse size triangular mesh is a good candidate for a fixed-size robot in a non-changing environment. Moreover, the varying size of the triangular mesh and grid cell representations are better choices for factories with changing plans and multi-robot sizes due to the effect of the inflation layer. Based on the definition of a metric, which is a criterion for quantifying the performance of path planning on a representation type, constant or variable size triangle shapes are the only and best candidate for discretization in about 59% of industrial environments. In other cases, both cell types, the square and the triangle, can together be the best representation

Impact of Workspace Decompositions on Discrete Search Leading Continuous Exploration (DSLX) Motion Planning

Abstract — We have recently proposed DSLX, a motion planner that significantly reduces the computational time for solving challenging kinodynamic problems by interleaving continuous state-space exploration with discrete search on a workspace decomposition. An important but inadequately understood aspect of DSLX is the role of the workspace decomposition on the computational efficiency of the planner. Understanding this role is important for successful applications of DSLX to increasingly complex robotic systems. This work shows that the granularity of the workspace decomposition directly impacts computational efficiency: DSLX is faster when the decomposition is neither too fine- nor too coarse-grained. Finding the right level of granularity can require extensive fine-tuning. This work demonstrates that significant computational efficiency can instead be obtained with no fine-tuning by using conforming Delaunay triangulations, which in the context of DSLX provide a natural workspace decomposition that allows an efficient interplay between continuous state-space exploration and discrete search. The results of this work are based on extensive experiments on DSLX using grid, trapezoidal, and triangular decompositions of various granularities to solve challenging first and second-order kinodynamic motion-planning problems. I