  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.
