Jerk-constrained trajectories offer a wide range of advantages that collectively improve the performance of robotic systems, including increased energy efficiency, durability, and safety. In this paper, we present a novel approach to jerk-constrained time-optimal trajectory planning (TOTP), which follows a specified path while satisfying up to third-order constraints to ensure safety and smooth motion. One significant challenge in jerk-constrained TOTP is a non-convex formulation arising from the inclusion of third-order constraints. Approximating inequality constraints can be particularly challenging because the resulting solutions may violate the actual constraints. We address this problem by leveraging convexity within the proposed formulation to form conservative inequality constraints. We then obtain the desired trajectories by solving an $\boldsymbol n$-dimensional Sequential Linear Program (SLP) iteratively until convergence. Lastly, we evaluate in a real robot the performance of trajectories generated with and without jerk limits in terms of peak power, torque efficiency, and tracking capability.

翻译：加加速度约束轨迹在提升机器人系统性能方面具有诸多优势，包括提高能源效率、耐久性和安全性。本文提出一种新颖的加加速度约束时间最优轨迹规划（TOTP）方法，该方法在满足三阶约束以确保安全和平滑运动的同时，沿指定路径执行轨迹规划。加加速度约束TOTP面临的核心挑战在于引入三阶约束导致的非凸建模问题。对不等式约束进行近似处理尤为困难，因为所得解可能违反实际约束。我们利用所提建模框架中的凸性构造保守不等式约束来解决该问题，随后通过迭代求解$\boldsymbol n$维序贯线性规划（SLP）直至收敛来获得期望轨迹。最后，在实际机器人上从峰值功率、转矩效率和轨迹跟踪能力三个维度，对含与不含加加速度限幅生成的轨迹性能进行了对比评估。