Collaborative Object Transportation in Space via Impact Interactions

TL;DR

This work tackles collaborative transportation of passive free-floating objects in microgravity by leveraging impact interactions between controllable robots. It introduces a hierarchical planning and control framework that combines an offline MILP planner using point-mass impact kinematics with Bézier-curve trajectories, an online replanner that adapts to updated states and refined impact models, and an impact-aware MPC for real-time tracking. A key contribution is the impact-robust planning objective, which maximizes post-impact velocity uncertainty $\\delta$ by propagating zonotopes, enabling resilience to model inaccuracies in impact dynamics. The approach is validated in high-fidelity simulations and hardware experiments on a 2-robot, 1-object free-flyer, including corridor transports, obstacle avoidance tasks, throw-and-catch, and pong-like sequences, demonstrating robust satisfaction of the spatial-temporal specifications. The resulting framework offers a scalable, energy-efficient paradigm for on-orbit servicing and space robotics where friction is negligible and impacts can be orchestrated to steer passive objects.

Abstract

We present a planning and control approach for collaborative transportation of objects in space by a team of robots. Object and robots in microgravity environments are not subject to friction but are instead free floating. This property is key to how we approach the transportation problem: the passive objects are controlled by impact interactions with the controlled robots. In particular, given a high-level Signal Temporal Logic (STL) specification of the transportation task, we synthesize motion plans for the robots to maximize the specification satisfaction in terms of spatial STL robustness. Given that the physical impact interactions are complex and hard to model precisely, we also present an alternative formulation maximizing the permissible uncertainty in a simplified kinematic impact model. We define the full planning and control stack required to solve the object transportation problem; an offline planner, an online replanner, and a low-level model-predictive control scheme for each of the robots. We show the method in a high-fidelity simulator for a variety of scenarios and present experimental validation of 2-robot, 1-object scenarios on a freeflyer platform.

Figures (11)

• Figure 1: An experimental platform with two controllable freeflyers and a passive object. To transport the object from the top of the figure to the bottom while avoiding the obstacle, Robot 1 impacts it to make it travel towards the top left corner, where Robot 2 impacts it to travel towards the bottom left corner, where it impacts it again to send it towards the right bottom corner where Robot 2 impacts it to reach its desired final destination. Impact times are shown as red stars.
• Figure 2: (a) Illustration of impact kinematics for point masses (according to Eq. \ref{['eq:robot_point_impact']}). The dashed and solid line indicate a trajectory of the object and robot respectively. Green and blue dots indicated endpoints of Bézier curves. The impact occurs after the first Bézier curve. (b) Impact kinematics for non-rotating cylindrical objects (according to Eq. \ref{['eq:robot_cylinder_impact']}). The moving blue object impacts a stationary green object. Both object's direction is changed according to the tangential and normal component of the impact on the boundaries of the objects.
• Figure 3: (a) a Bézier curve with its control points (red dots) and convex hull (shaded blue), (b) a trajectory of robot $R_i$ with three Bézier curves. Note the bounding-box used for collision avoidance, (c) the Bézier trajectory formulation for objects (first degree Bézier curves) and robots (higher-degree Bézier curves and continuity conditions). $r_{R_1}(0)$ and $r_{R_1}(1)$ are the pre- and post-impact curves of impact $1$. $r_{R_1}(1)$ and $r_{R_1}(2)$ are the pre- and post-impact curves of impact $2$.
• Figure 4: An example corridor travel scenario with (a) the problem setup with 2 robots ($R_1$ and $R_2$) and one object ($O_1$). The objective is to transport $O_1$ to goal while all systems should avoid the red obstacles. (b) the spatially-robust plan from the offline planner in \ref{['ssec:method_best_case']} with two impacts denoted by $I_1$ and $I_2$. (c) the vertical position over time. (d) the vertical velocity over time. Notice that the velocity (and therefore position) of $O_1$ can only be changed via impacts with $R_1$ or $R_2$. The change in velocity is instantaneous, according to the impact kinematics in Eq. \ref{['eq:robot_point_impact']}.
• Figure 5: An example corridor travel scenario with (a) the problem setup with 2 robots ($R_1$ and $R_2$) and one object ($O_1$). The objective is to transport $O_1$ to goal while all systems should avoid the red obstacles. (b) the impact-robust plan from the offline planner in \ref{['ssec:method_worst_case']}. Three planned impacts are indicated by $I_1$, $I_2$ and $I_3$. Instead of a deterministic state for $O_1$ as in Fig. \ref{['fig:corridor_space_robust']}, the post-impact states are now represented by zonotopes and the robot trajectories consider the traversal to all extremal vertices. (c) the vertical position over time. Impact $I_2$ at $t\approx 45s$ creates a decreasing funnel indicating that the overall uncertainty in the system can be reduced by additional impacts (as all $v \in \hat{Z}_{O}$ have a unique impact). (d) the vertical velocity over time. Notice that the velocity (and therefore position) of $O_1$ can only be changed via impacts with $R_1$ or $R_2$ and that any impact between $O_1$ and $R_i$ introduces the propagation of a funnel due to the uncertain post-impact term $\delta$. Note the constant time duration of of the zonotope segments of the object in (c) and (d).

Theorems & Definitions (6)

• Definition 1: Time-bounded STL
• Example 1
• Example 2
• Lemma 1
• Example 3
• Remark 1