Trajectory Generation

Trajectory Planning of Unicycle Mobile Robots With a Trapezoidal-Velocity Constraint

“…It is based on 1) the partition of the operational path into continuous-curvature portions, alternating corner-type and linear-type portions; 2) the choice of the extremities of these portions as a subset of free-control nodes; and 3) the choice of a piecewise trapezoidal profile for linear and angular velocities along each portion. Note that we could have avoided discontinuities in torques by using instead a so-called smoothed TVP [13], [14]. This can be achieved (with the same number of free parameters and a relatively small additional runtime) by modeling both v(ξ) and ω(ξ) using cubic functions within the acceleration/deceleration phases of each portion while requiring the continuity of v(ξ), ω(ξ), (dv/dξ), and (dω/dξ) along the whole trajectory.…”

“…Nonetheless, as dynamic constraints, such as those on maximum torques, are not included, the practicability of the trajectories thus calculated may become a serious problem. To answer this need, a variant of RPA was proposed in [13]. This variant, which we call RTVPA, combines the interesting features of both RPA and TVP generators.…”

“…Compared with RPA, it is able to find solutions of almost similar quality but in much shorter runtimes. For instance, a minimum-time problem for a 6-DOF FBM under constraints on dynamics is solved in less than 2 s on a 2.5-GHz PC [13], [14]. However, this variant is limited to the case of an FBM and does not handle obstacle avoidance.…”