On smooth and safe trajectory planning in 2D environments

Abstract

A novel approach to generating optimal smooth piecewise trajectories based o n a new energy memure i s proposed. Given the configurations (position and direction) of two points in the plane, we search for the minimal energy trajectory that minimizes the integral of the squared acceleration opposed to curvature, which has been the predominant energy measure studied in the literature. The smoothness of the optimal trajectory depends on how the tangential and normal components of acceleration vary over a n interval of time. A numerical iterative procedure is devised for computing the optimal piecewise trajectory as a solution of a constmined boundary value problem. The resulting trajectories are not only smooth but also safe wtth optimal velocity (acceleration) profiles and therefore suitable for robot motion planning applications.The feasibility of the proposed approach is illustrated by several simulation examples. Besides motion planning, the resulting trajectories may be useful in wmputer graphics and geometric design.

Investigating the Impact of Energy Source Level on the Self-Guided Vehicle System Performances, in the Industry 4.0 Context

“…Path smoothness is also an important aspect of planning energy-efficient trajectory. In [52], the authors proposed an optimal smooth and minimal energy trajectory by minimizing the normal and tangential acceleration variation over an interval of time. The work presented in [53] compares trajectories in terms of energy consumption.…”

Time-Energy Optimal Cluster Space Motion Planning for Mobile Robot Formations

“…This analysis is then used to generate both an energy optimal path and a velocity trajectory, which further conserves energy. While a complete and detailed energy model can be beneficial, it is well known that preventing large torque variations in motors by smoothing velocity profiles is most fundamental to energy conservation [42,43]. This chapter concentrates on minimizing energy expenditure for a formation of mobile robots in this regard.…”

Energy-Efficient Trajectory Planning for a Mobile Agent by Using a Two-Stage Decomposition Approach

“…Timeoptimal trajectory planning of a mobile agent was studied in Lau et al [2009], where the generated trajectory has continuous curvature. The change of trajectory curvature was also used as the smoothness criterion in the trajectory planning Hussein and Elnagar [1997]. It was reported that the energy consumption could be minimized through optimizing the control inputs along the trajectory Guo andTang [2008]-Howard andKelly [2007], subject to boundary conditions of arrival time and velocity/acceleration at the start and end positions.…”