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.

Optimal motion planning along prescribed paths can be solved with several techniques, but most of them do not take into account the wrenches exerted by the end-effector when in contact with the environment. When a dynamic model of the environment is not available, no consolidated methodology exists to consider the effect of the interaction. Regardless of the specific performance index to optimize, this article proposes a strategy to include external wrenches in the optimal planning algorithm, considering the task specifications. This procedure is instantiated for minimum-time trajectories and validated on a real robot performing an interaction task under admittance control. The results prove that the inclusion of end-effector wrenches affect the planned trajectory, in fact modifying the manipulator's dynamic capability.

Basis splines enable a time-continuous feasibility check with a finite number of constraints. Constraints apply to the whole trajectory for motion planning applications that require a collision-free and dynamically feasible trajectory. Existing motion planners that rely on gradient-based optimization apply time scaling to implement a shrinking planning horizon. They neither guarantee a recursively feasible trajectory nor enable reaching two terminal manifold parts at different time scales. This paper proposes a nonlinear optimization problem that addresses the drawbacks of existing approaches. Therefore, the spline breakpoints are included in the optimization variables. Transformations between spline bases are implemented so a sparse problem formulation is achieved. A strategy for breakpoint removal enables the convergence into a terminal manifold. The evaluation in an overtaking scenario shows the influence of the breakpoint number on the solution quality and the time required for optimization.