DisCo: Distributed Contact-Rich Trajectory Optimization for Forceful Multi-Robot Collaboration

TL;DR

DisCo is a distributed contact-implicit trajectory optimization algorithm, which allows a group of robots to optimize a time sequence of forces to objects and to their environment to accomplish tasks such as collaborative manipulation, robot team sports, and modular robot locomotion.

Abstract

We present DisCo, a distributed algorithm for contact-rich, multi-robot tasks. DisCo is a distributed contact-implicit trajectory optimization algorithm, which allows a group of robots to optimize a time sequence of forces to objects and to their environment to accomplish tasks such as collaborative manipulation, robot team sports, and modular robot locomotion. We build our algorithm on a variant of the Alternating Direction Method of Multipliers (ADMM), where each robot computes its own contact forces and contact-switching events from a smaller single-robot, contact-implicit trajectory optimization problem, while cooperating with other robots through dual variables, enforcing constraints between robots. Each robot iterates between solving its local problem, and communicating over a wireless mesh network to enforce these consistency constraints with its neighbors, ultimately converging to a coordinated plan for the group. The local problems solved by each robot are significantly less challenging than a centralized problem with all robots' contact forces and switching events, improving the computational efficiency, while also preserving the privacy of some aspects of each robot's operation. We demonstrate the effectiveness of our algorithm in simulations of collaborative manipulation, multi-robot team sports scenarios, and in modular robot locomotion, where DisCo achieves $3$x higher success rates with a 2.5x to 5x faster computation time. Further, we provide results of hardware experiments on a modular truss robot, with three collaborating truss nodes planning individually while working together to produce a punctuated rolling-gate motion of the composite structure. Videos are available on the project page: https://disco-opt.github.io.

Figures (12)

• Figure 1: Our algorithm, DisCo, is amenable to a broad class of collaborative multi-robot problems involving contact, such as: (Left) collaborative manipulation, e.g., of a table; (Center) robot team sports, e.g., robot soccer; and (Right) locomotion of modular robots, e.g., usevitch_untethered_2020. In each scenario, each robot solves a smaller contact-implicit trajectory optimization problem to complete the task in collaboration with other robots.
• Figure 2: The Coulomb friction cone and its polygonal approximation with $m$ tangential directions denoted by $\nu_{1},\ldots,\nu_{m}$.
• Figure 3: The contact impulses $c$ and $\alpha$, initially expressed in a local reference frame attached to the end-effector of the robot, are transformed to the inertial frame, displayed in the lower-left corner.
• Figure 4: A group of $4$ robots (in red) manipulate a rod (in blue) by sliding it along the ground to a desired position and orientation (in gray). The robots begin from arbitrary locations around the rod. (Center) They approach and contact the rod to form a stable grasp, sliding the rod along the ground. (Right) They bring the object to rest at the desired configuration.
• Figure 5: The normal components (top) and tangential components (bottom) of the contact forces applied by each robot, as $16$ robots slide a rod to a desired position and orientation along a surface, showing the discrete contact interactions between each robot and the object as the object slides along its surface.

Theorems & Definitions (6)

• Proposition 1
• proof
• Remark 1
• Remark 2
• Theorem 1
• proof