A randomized kinodynamic planner for closed-chain robotic systems

Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin

Approximate Euclidean shortest paths in polygonal domains

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input parameter $\epsilon$. We utilize $\Omega$ to compute a $(1+\epsilon)$-approximate geodesic shortest path between the two given points in $O(n + h((\lg{n}) + (\lg{h})^{1+\delta} + (\frac{1}{\epsilon}\lg{\frac{h}{\epsilon}})))$ time. Here, $\epsilon$ is a user parameter, and $\delta$ is a small positive constant (resulting from the time for triangulating the free space of $\cal P$ using the algorithm in \cite{journals/ijcga/Bar-YehudaC94}). Moreover, we devise a $(2+\epsilon)$-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.Comment: a few updates; accepted to ISAAC 201

Algorithms for Monotone Paths with Visibility Properties

Constructing collision-free paths in Euclidean space is a well-known problem in computational geometry having applications in many fields that include robotics, VLSI, and covert surveillance. In this thesis, we investigate the development of efficient algorithms for constructing a collision-free path that satisfies directional and visibility constraints. We present algorithms for constructing monotone collision-free paths that tend to maximize the visibility of the boundary of obstacles. We also present implementation of some monotone path planning algorithms in Java Programming Language

Collision avoidance and dynamic modeling for wheeled mobile robots and industrial manipulators

Collision Avoidance and Dynamic Modeling are key topics for researchers dealing with mobile and industrial robotics. A wide variety of algorithms, approaches and methodologies have been exploited, designed or adapted to tackle the problems of finding safe trajectories for mobile robots and industrial manipulators, and of calculating reliable dynamics models able to capture expected and possible also unexpected behaviors of robots. The knowledge of these two aspects and their potential is important to ensure the efficient and correct functioning of Industry 4.0 plants such as automated warehouses, autonomous surveillance systems and assembly lines. Collision avoidance is a crucial aspect to improve automation and safety, and to solve the problem of planning collision-free trajectories in systems composed of multiple autonomous agents such as unmanned mobile robots and manipulators with several degrees of freedom. A rigorous and accurate model explaining the dynamics of robots, is necessary to tackle tasks such as simulation, torque estimation, reduction of mechanical vibrations and design of control law