Real-Time Acceleration-Continuous Path-Constrained Trajectory Planning With Built-In Tradeoff Between Cruise and Time-Optimal Motions

Abstract

In this paper, a novel real-time accelerationcontinuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradability mechanism between cruise motion and time-optimal motion. Different from existing approaches, the proposed approach smoothens timeoptimal trajectories with bang-bang input structures to generate acceleration-continuous trajectories while preserving the completeness property. More importantly, a novel built-in tradability mechanism is proposed and embedded into the trajectory planning framework, so that the proportion of the cruise motion and time-optimal motion can be flexibly adjusted by changing a userspecified functional parameter. Thus, the user can easily apply the trajectory planning algorithm for various tasks with different requirements on motion efficiency and cruise proportion. Moreover, it is shown that feasible trajectories are computed more quickly than optimal trajectories. Rigorous mathematical analysis and proofs are provided for these aforementioned results. Comparative simulation and experimental results on omnidirectional wheeled mobile robots demonstrate the capability of the proposed algorithm in terms of flexible tunning between cruise and timeoptimal motions, as well as higher computational efficiency.

E 3 MoP: Efficient Motion Planning Based on Heuristic-Guided Motion Primitives Pruning and Path Optimization With Sparse-Banded Structure

“…Finally, a numerical integration (NI)-based time-optimal velocity planning algorithm presented in [14] is employed to generate a feasible linear velocity profile along the smoothed local path. The NI-based algorithm can acquire provably time-optimal trajectory with low computational complexity [43]- [46], which solves the problem by computing maximum velocity curve (MVC) considering both kinematic and environmental constraints and then performing numerical integration under MVC. Readers can refer to [14] for more details about the proofs of feasibility, completeness, and timeoptimality of this algorithm.…”

E$ \mathbf{^3} $MoP: Efficient Motion Planning Based on Heuristic-Guided Motion Primitives Pruning and Path Optimization With Sparse-Banded Structure

“…Finally, a numerical integration-based velocity planning algorithm described in [9] is utilized to generate a feasible linear velocity profile along the smoothed local path under the velocity and acceleration constraints. According to [25]- [27], numerical integration-based velocity planning can generate time-optimal trajectory with lower computational complexity. Compared with the sampling-based local planning approaches mentioned above, the proposed local planner achieves better performance in terms of motion efficiency, smoothness, and flexibility.…”

Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

“…This translates into intuitive design methods. However, it is important to note that when expressed in Fourier series, all synthesized trajectories -such as those based on polynomial (Analooee et al, 2020;Shen et al, 2020), Akima (Bica, 2014;Wang et al, 2014), or B spline (Du et al, 2018;Simba et al, 2016) curves -contain significant high-harmonic content. In addition, the nonlinearity of the machine system dynamics would require actuating forces/torques with even higher-harmonic content to follow the prescribed trajectories.…”