Collision-free and smooth trajectory computation in cluttered environments

Abstract

We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by samplebased motion planners. Our approach uses cubic B-splines to generate trajectories which are C 2 almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in environments with narrow passages. We also present a fast and reliable algorithm for collision checking between robot and the environment along the B-spline trajectories. We highlight the performance of our algorithm on complex benchmarks, including path computation for rigid and articulated models in cluttered environments.

Polynomial Trajectory Planning for Aggressive Quadrotor Flight in Dense Indoor Environments

“…The polynomial is re-optimized with the additional waypoint, and the process is repeated if necessary until the polynomial trajectory is collision free. A similar technique is used in [23]. Figure 4 illustrates this process successfully resolving a collision.…”

Motion planning with sequential convex optimization and convex collision checking

“…Shortcut-based methods (Kallmann et al, 2003;Hauser and Ng-Thow-Hing, 2010;Pan et al, 2012) replace non-smooth portions of a trajectory shorter linear or curved segments (e.g. parabolic arcs, Bézier curves).…”

Stochastic Extended LQR: Optimization-Based Motion Planning Under Uncertainty

“…Optimization-based approaches have been developed that plan from scratch as well as that locally optimize a feasible plan created by another motion planner (such as a sampling-based motion planner), e.g. [29], [7], [18], [3], [5], [11]. These methods work well for robots with deterministic dynamics, whereas SELQR is intended for robots with stochastic dynamics.…”

“…With the inverse control policy from the last forward pass, SELQR computes û t and x̂t (line 15), around which the stochastic discrete dynamics can be linearized as (11) where denotes the i'th column of matrix M t , and A t , B t , , , a t , and are given matrices and vectors of the appropriate dimension, and the cost function c t can be quadratized as (12) By substituting the linear stochastic dynamics and quadratic local cost function into Eq. 8, expanding the expectation, and then collecting terms, we get a quadratic expression of the value function v t (x), (13) Sun et al Page 7 where following the similar derivation in [21].…”