333 research outputs found
Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems
This paper presents a systematic approach for computing local solutions to
motion planning problems in non-convex environments using numerical optimal
control techniques. It extends the range of use of state-of-the-art numerical
optimal control tools to problem classes where these tools have previously not
been applicable. Today these problems are typically solved using motion
planners based on randomized or graph search. The general principle is to
define a homotopy that perturbs, or preferably relaxes, the original problem to
an easily solved problem. By combining a Sequential Quadratic Programming (SQP)
method with a homotopy approach that gradually transforms the problem from a
relaxed one to the original one, practically relevant locally optimal solutions
to the motion planning problem can be computed. The approach is demonstrated in
motion planning problems in challenging 2D and 3D environments, where the
presented method significantly outperforms a state-of-the-art open-source
optimizing sampled-based planner commonly used as benchmark
CTopPRM: Clustering Topological PRM for Planning Multiple Distinct Paths in 3D Environments
In this paper, we propose a new method called Clustering Topological PRM
(CTopPRM) for finding multiple homotopically distinct paths in 3D cluttered
environments. Finding such distinct paths, e.g., going around an obstacle from
a different side, is useful in many applications. Among others, using multiple
distinct paths is necessary for optimization-based trajectory planners where
found trajectories are restricted to only a single homotopy class of a given
path. Distinct paths can also be used to guide sampling-based motion planning
and thus increase the effectiveness of planning in environments with narrow
passages. Graph-based representation called roadmap is a common representation
for path planning and also for finding multiple distinct paths. However,
challenging environments with multiple narrow passages require a densely
sampled roadmap to capture the connectivity of the environment. Searching such
a dense roadmap for multiple paths is computationally too expensive. Therefore,
the majority of existing methods construct only a sparse roadmap which,
however, struggles to find all distinct paths in challenging environments. To
this end, we propose the CTopPRM which creates a sparse graph by clustering an
initially sampled dense roadmap. Such a reduced roadmap allows fast
identification of homotopically distinct paths captured in the dense roadmap.
We show, that compared to the existing methods the CTopPRM improves the
probability of finding all distinct paths by almost 20% in tested environments,
during same run-time. The source code of our method is released as an
open-source package.Comment: in IEEE Robotics and Automation Letter
Robot Motion Planning Under Topological Constraints
My thesis addresses the the problem of manipulation using multiple robots with cables. I study how robots with cables can tow objects in the plane, on the ground and on water, and how they can carry suspended payloads in the air. Specifically, I focus on planning optimal trajectories for robots.
Path planning or trajectory generation for robotic systems is an active area of research in robotics. Many algorithms have been developed to generate path or trajectory for different robotic systems. One can classify planning algorithms into two broad categories. The first one is graph-search based motion planning over discretized configuration spaces. These algorithms are complete and quite efficient for finding optimal paths in cluttered 2-D and 3-D environments and are widely used [48]. The other class of algorithms are optimal control based methods. In most cases, the optimal control problem to generate optimal trajectories can be framed as a nonlinear and non convex optimization problem which is hard to solve. Recent work has attempted to overcome these shortcomings [68]. Advances in computational power and more sophisticated optimization algorithms have allowed us to solve more complex problems faster. However, our main interest is incorporating topological constraints. Topological constraints naturally arise when cables are used to wrap around objects. They are also important when robots have to move one way around the obstacles rather than the other way around. Thus I consider the optimal trajectory generation problem under topological constraints, and pursue problems that can be solved in finite-time, guaranteeing global optimal solutions.
In my thesis, I first consider the problem of planning optimal trajectories around obstacles using optimal control methodologies. I then present the mathematical framework and algorithms for multi-robot topological exploration of unknown environments in which the main goal is to identify the different topological classes of paths. Finally, I address the manipulation and transportation of multiple objects with cables. Here I consider teams of two or three ground robots towing objects on the ground, two or three aerial robots carrying a suspended payload, and two boats towing a boom with applications to oil skimming and clean up. In all these problems, it is important to consider the topological constraints on the cable configurations as well as those on the paths of robot. I present solutions to the trajectory generation problem for all of these problems
Distributed Formation Control for Multi-Vehicle Systems With Splitting and Merging Capability
This letter develops a novel strategy for splitting and merging of agents travelling in formation. The method converts the formation control problem into an optimization problem, which is solved among the agents in a distributed fashion. The proposed control strategy is one type of Distributed Model Predictive Control (DMPC) which allows the system to cope with disturbances and dynamic environments. A modified Alternating Direction Method of Multipliers (ADMM) is designed to solve the trajectory optimization problem and achieve formation scaling. Furthermore, a mechanism is designed to implement path homotopy in splitting and merging of the formation, which examines the H-signature of the generated trajectories. Simulation shows that, by using the proposed method, the formation is able to automatically resize and dynamically split to better avoid obstacles, even in the case of losing communication among agents. Upon splitting the newly formed groups proceed and merge again when it becomes possible
Off the Beaten Track: Laterally Weighted Motion Planning for Local Obstacle Avoidance
We extend the behaviour of generic sample-based motion planners to support
obstacle avoidance during long-range path following by introducing a new
edge-cost metric paired with a curvilinear planning space. The resulting
planner generates naturally smooth paths that avoid local obstacles while
minimizing lateral path deviation to best exploit prior terrain knowledge from
the reference path. In this adaptation, we explore the nuances of planning in
the curvilinear configuration space and describe a mechanism for natural
singularity handling to improve generality. We then shift our focus to the
trajectory generation problem, proposing a novel Model Predictive Control (MPC)
architecture to best exploit our path planner for improved obstacle avoidance.
Through rigorous field robotics trials over 5 km, we compare our approach to
the more common direct path-tracking MPC method and discuss the promise of
these techniques for reliable long-term autonomous operations.Comment: 15 pages, 21 Figures, 3 Tables. Manuscript was submitted to IEEE
Transactions on Robotics on September 17th, 202
Near-Optimal Motion Planning Algorithms Via A Topological and Geometric Perspective
Motion planning is a fundamental problem in robotics, which involves finding a path for an autonomous system, such as a robot, from a given source to a destination while avoiding collisions with obstacles. The properties of the planning space heavily influence the performance of existing motion planning algorithms, which can pose significant challenges in handling complex regions, such as narrow passages or cluttered environments, even for simple objects. The problem of motion planning becomes deterministic if the details of the space are fully known, which is often difficult to achieve in constantly changing environments. Sampling-based algorithms are widely used among motion planning paradigms because they capture the topology of space into a roadmap. These planners have successfully solved high-dimensional planning problems with a probabilistic-complete guarantee, i.e., it guarantees to find a path if one exists as the number of vertices goes to infinity. Despite their progress, these methods have failed to optimize the sub-region information of the environment for reuse by other planners. This results in re-planning overhead at each execution, affecting the performance complexity for computation time and memory space usage.
In this research, we address the problem by focusing on the theoretical foundation of the algorithmic approach that leverages the strengths of sampling-based motion planners and the Topological Data Analysis methods to extract intricate properties of the environment. The work contributes a novel algorithm to overcome the performance shortcomings of existing motion planners by capturing and preserving the essential topological and geometric features to generate a homotopy-equivalent roadmap of the environment. This roadmap provides a mathematically rich representation of the environment, including an approximate measure of the collision-free space. In addition, the roadmap graph vertices sampled close to the obstacles exhibit advantages when navigating through narrow passages and cluttered environments, making obstacle-avoidance path planning significantly more efficient.
The application of the proposed algorithms solves motion planning problems, such as sub-optimal planning, diverse path planning, and fault-tolerant planning, by demonstrating the improvement in computational performance and path quality. Furthermore, we explore the potential of these algorithms in solving computational biology problems, particularly in finding optimal binding positions for protein-ligand or protein-protein interactions.
Overall, our work contributes a new way to classify routes in higher dimensional space and shows promising results for high-dimensional robots, such as articulated linkage robots. The findings of this research provide a comprehensive solution to motion planning problems and offer a new perspective on solving computational biology problems
On Randomized Path Coverage of Configuration Spaces
We present a sampling-based algorithm that generates a set of locally-optimal paths that differ in visibility
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