Planning Optimal Trajectories for Mobile Manipulators under End-effector Trajectory Continuity Constraint

TL;DR

This paper tackles the mobile manipulator motion planning problem under the end-effector trajectory continuity constraint in which the end-effector is required to traverse a continuous task-space trajectory (time-parametrized path), such as in mobile printing or spraying applications.

Abstract

Mobile manipulators have been employed in many applications that are traditionally performed by either multiple fixed-base robots or a large robotic system. This capability is enabled by the mobility of the mobile base. However, the mobile base also brings redundancy to the system, which makes mobile manipulator motion planning more challenging. In this paper, we tackle the mobile manipulator motion planning problem under the end-effector trajectory continuity constraint in which the end-effector is required to traverse a continuous task-space trajectory (time-parametrized path), such as in mobile printing or spraying applications. Our method decouples the problem into: (1) planning an optimal base trajectory subject to geometric task constraints, end-effector trajectory continuity constraint, collision avoidance, and base velocity constraint; which ensures that (2) a manipulator trajectory is computed subsequently based on the obtained base trajectory. To validate our method, we propose a discrete optimal base trajectory planning algorithm to solve several mobile printing tasks in hardware experiment and simulations.

Figures (8)

• Figure 1: Mobile 3D printing of NTU shape (10 layers, size: $3 \times 0.75 \times 0.15m$, total printing path length: 112.9m) with constant nozzle speed of $10cm/s$.
• Figure 2: Visualization of a trajectory in the base configuration spacetime (B-spacetime). The base orientation $\varphi$ axis is not shown. Any point $\mathbf{x}(s)$ in the trajectory must be inside an admissible B-space $\mathcal{B}_a(t)$ and its velocity $\dot{\mathbf{x}}(s)$ must be inside a cone of admissible spacetime velocities $\mathcal{V}_a$. The admissible B-spacetime $\mathcal{X}_a$ is obtained as the admissible B-space changes in time.
• Figure 3: Visualization of Kinematic Reachability Analysis
• Figure 4: Discretized admissible B-space $\mathcal{B}_a(0)$ for end-effector pose $\mathbf{p}(0)$. The vertical axis shows $\varphi \in (-\pi,\pi]$ for $\varphi \in \mathbb{S}^1$ while time axis is not shown.
• Figure 5: Mobile 1D printing a $2.1m$-long line with different base's DOFs. (a) and (b) are seen in B-spacetime, (c) is seen in task space.

Theorems & Definitions (4)

• Definition 1: One-step feasible set
• Definition 2: i-stage feasible set
• Theorem 1: Completeness
• Theorem 2: Optimality