SUMMARYThe Tangent Bundle Rapidly Exploring Random Tree (TB-RRT) is an algorithm for planning robot motions on curved configuration space manifolds, in which the key idea is to construct random trees not on the manifold itself, but on tangent bundle approximations to the manifold. Curvature-based methods are developed for constructing tangent bundle approximations, and procedures for random node generation and bidirectional tree extension are developed that significantly reduce the number of projections to the manifold. Extensive numerical experiments for a wide range of planning problems demonstrate the computational advantages of the TB-RRT algorithm over existing constrained path planning algorithms.

No abstract

Given a vector field defined on a robot's configuration space, in which the vector field represents the system drift, e.g. a wind velocity field, water current flow, or gradient field for some potential function, we present a randomized path planning algorithm for reaching a desired goal configuration. Taking the premise that moving against the vector field requires greater control effort, and that minimizing the control effort is both physically meaningful and desirable, we propose an integral functional for control effort, called the upstream criterion, that measures the extent to which a path goes against the given vector field. The integrand of the upstream criterion is then used to construct a rapidly exploring random tree (RRT) in the configuration space, in a way such that random nodes are generated with an a priori specified bias that favors directions indicated by the vector field. The resulting planning algorithm produces better quality paths while preserving many of the desirable features of RRT-based planning, e.g. the Voronoi bias property, computational efficiency, algorithmic simplicity, and straightforward extension to constrained and nonholonomic problems. Extensive numerical experiments demonstrate the advantages of our algorithm vis-à-vis existing optimality criterion-based planning algorithms.

We provide a tutorial and review of the state-of-the-art in robot dynamics algorithms that rely on methods from differential geometry, particularly the theory of Lie groups. After reviewing the underlying Lie group structure of the rigid-body motions and the geometric formulation of the equations of motion for a single rigid body, we show how classical screw-theoretic concepts can be expressed in a reference frame-invariant way using Lie-theoretic concepts and derive recursive algorithms for the forward and inverse dynamics and their differentiation. These algorithms are extended to robots subject to closed-loop and other constraints, joints driven by variable stiffness actuators, and also to the modeling of contact between rigid bodies. We conclude with a demonstration of how the geometric formulations and algorithms can be effectively used for robot motion optimization.

No abstract