5,438 research outputs found
Incremental Sampling-based Algorithm for Minimum-violation Motion Planning
This paper studies the problem of control strategy synthesis for dynamical
systems with differential constraints to fulfill a given reachability goal
while satisfying a set of safety rules. Particular attention is devoted to
goals that become feasible only if a subset of the safety rules are violated.
The proposed algorithm computes a control law, that minimizes the level of
unsafety while the desired goal is guaranteed to be reached. This problem is
motivated by an autonomous car navigating an urban environment while following
rules of the road such as "always travel in right lane'' and "do not change
lanes frequently''. Ideas behind sampling based motion-planning algorithms,
such as Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees
(RRTs), are employed to incrementally construct a finite concretization of the
dynamics as a durational Kripke structure. In conjunction with this, a weighted
finite automaton that captures the safety rules is used in order to find an
optimal trajectory that minimizes the violation of safety rules. We prove that
the proposed algorithm guarantees asymptotic optimality, i.e., almost-sure
convergence to optimal solutions. We present results of simulation experiments
and an implementation on an autonomous urban mobility-on-demand system.Comment: 8 pages, final version submitted to CDC '1
Search-based 3D Planning and Trajectory Optimization for Safe Micro Aerial Vehicle Flight Under Sensor Visibility Constraints
Safe navigation of Micro Aerial Vehicles (MAVs) requires not only
obstacle-free flight paths according to a static environment map, but also the
perception of and reaction to previously unknown and dynamic objects. This
implies that the onboard sensors cover the current flight direction. Due to the
limited payload of MAVs, full sensor coverage of the environment has to be
traded off with flight time. Thus, often only a part of the environment is
covered.
We present a combined allocentric complete planning and trajectory
optimization approach taking these sensor visibility constraints into account.
The optimized trajectories yield flight paths within the apex angle of a
Velodyne Puck Lite 3D laser scanner enabling low-level collision avoidance to
perceive obstacles in the flight direction. Furthermore, the optimized
trajectories take the flight dynamics into account and contain the velocities
and accelerations along the path.
We evaluate our approach with a DJI Matrice 600 MAV and in simulation
employing hardware-in-the-loop.Comment: In Proceedings of IEEE International Conference on Robotics and
Automation (ICRA), Montreal, Canada, May 201
Optimization Model for Planning Precision Grasps with Multi-Fingered Hands
Precision grasps with multi-fingered hands are important for precise
placement and in-hand manipulation tasks. Searching precision grasps on the
object represented by point cloud, is challenging due to the complex object
shape, high-dimensionality, collision and undesired properties of the sensing
and positioning. This paper proposes an optimization model to search for
precision grasps with multi-fingered hands. The model takes noisy point cloud
of the object as input and optimizes the grasp quality by iteratively searching
for the palm pose and finger joints positions. The collision between the hand
and the object is approximated and penalized by a series of least-squares. The
collision approximation is able to handle the point cloud representation of the
objects with complex shapes. The proposed optimization model is able to locate
collision-free optimal precision grasps efficiently. The average computation
time is 0.50 sec/grasp. The searching is robust to the incompleteness and noise
of the point cloud. The effectiveness of the algorithm is demonstrated by
experiments.Comment: Submitted to IROS2019, experiment on BarrettHand, 8 page
Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments
In this paper, we address the risk estimation problem where one aims at
estimating the probability of violation of safety constraints for a robot in
the presence of bounded uncertainties with arbitrary probability distributions.
In this problem, an unsafe set is described by level sets of polynomials that
is, in general, a non-convex set. Uncertainty arises due to the probabilistic
parameters of the unsafe set and probabilistic states of the robot. To solve
this problem, we use a moment-based representation of probability
distributions. We describe upper and lower bounds of the risk in terms of a
linear weighted sum of the moments. Weights are coefficients of a univariate
Chebyshev polynomial obtained by solving a sum-of-squares optimization problem
in the offline step. Hence, given a finite number of moments of probability
distributions, risk can be estimated in real-time. We demonstrate the
performance of the provided approach by solving probabilistic collision
checking problems where we aim to find the probability of collision of a robot
with a non-convex obstacle in the presence of probabilistic uncertainties in
the location of the robot and size, location, and geometry of the obstacle.Comment: 57th IEEE Conference on Decision and Control 201
Sampling-based Algorithms for Optimal Motion Planning
During the last decade, sampling-based path planning algorithms, such as
Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have
been shown to work well in practice and possess theoretical guarantees such as
probabilistic completeness. However, little effort has been devoted to the
formal analysis of the quality of the solution returned by such algorithms,
e.g., as a function of the number of samples. The purpose of this paper is to
fill this gap, by rigorously analyzing the asymptotic behavior of the cost of
the solution returned by stochastic sampling-based algorithms as the number of
samples increases. A number of negative results are provided, characterizing
existing algorithms, e.g., showing that, under mild technical conditions, the
cost of the solution returned by broadly used sampling-based algorithms
converges almost surely to a non-optimal value. The main contribution of the
paper is the introduction of new algorithms, namely, PRM* and RRT*, which are
provably asymptotically optimal, i.e., such that the cost of the returned
solution converges almost surely to the optimum. Moreover, it is shown that the
computational complexity of the new algorithms is within a constant factor of
that of their probabilistically complete (but not asymptotically optimal)
counterparts. The analysis in this paper hinges on novel connections between
stochastic sampling-based path planning algorithms and the theory of random
geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics
Researc
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
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