2,271 research outputs found
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
Downwash-Aware Trajectory Planning for Large Quadrotor Teams
We describe a method for formation-change trajectory planning for large
quadrotor teams in obstacle-rich environments. Our method decomposes the
planning problem into two stages: a discrete planner operating on a graph
representation of the workspace, and a continuous refinement that converts the
non-smooth graph plan into a set of C^k-continuous trajectories, locally
optimizing an integral-squared-derivative cost. We account for the downwash
effect, allowing safe flight in dense formations. We demonstrate the
computational efficiency in simulation with up to 200 robots and the physical
plausibility with an experiment with 32 nano-quadrotors. Our approach can
compute safe and smooth trajectories for hundreds of quadrotors in dense
environments with obstacles in a few minutes.Comment: 8 page
On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages
We extend our study of Motion Planning via Manifold Samples (MMS), a general
algorithmic framework that combines geometric methods for the exact and
complete analysis of low-dimensional configuration spaces with sampling-based
approaches that are appropriate for higher dimensions. The framework explores
the configuration space by taking samples that are entire low-dimensional
manifolds of the configuration space capturing its connectivity much better
than isolated point samples. The contributions of this paper are as follows:
(i) We present a recursive application of MMS in a six-dimensional
configuration space, enabling the coordination of two polygonal robots
translating and rotating amidst polygonal obstacles. In the adduced experiments
for the more demanding test cases MMS clearly outperforms PRM, with over
20-fold speedup in a coordination-tight setting. (ii) A probabilistic
completeness proof for the most prevalent case, namely MMS with samples that
are affine subspaces. (iii) A closer examination of the test cases reveals that
MMS has, in comparison to standard sampling-based algorithms, a significant
advantage in scenarios containing high-dimensional narrow passages. This
provokes a novel characterization of narrow passages which attempts to capture
their dimensionality, an attribute that had been (to a large extent) unattended
in previous definitions.Comment: 20 page
A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints
Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima
- …