Autonomous Robust Manipulation via Optimization with Uncertainty-aware Reachability

Can’t Touch This: Real-Time, Safe Motion Planning and Control for Manipulators Under Uncertainty

Jonathan Michaux

Patrick Holmes

Bohao Zhang

Che Chen

Baiyue Wang

Shrey Sahgal

Tiancheng Zhang

Sidhartha Dey

Shreyas Kousik

Ram Vasudevan

Paper

Appendix-F

Code

Introduction

A key challenge to the widespread deployment of robotic manipulators is the need to ensure safety in arbitrary environments while generating new motion plans in real-time. In particular, one must ensure that the manipulator does not collide with obstacles, collide with itself, or exceed its own joint torque limits. This challenge is compounded by the need to account for uncertainty in the mass and inertia of manipulated objects, and potentially the robot itself. The present work addresses this challenge by proposing Autonomous Robust Manipulation via Optimization with Uncertainty-aware Reachability ARMOUR, a provably-safe, receding-horizon trajectory planner and tracking controller framework for serial link manipulators. In particular, this paper makes three contributions. First, a robust, passivity-based controller enables a manipulator to track desired trajectories with bounded error despite uncertain dynamics. Second, a novel variation on the Recursive Newton-Euler Algorithm (RNEA) allows \methodname to compute the set of all possible inputs required to track any trajectory within a continuum of desired trajectories. Third, this paper provides a method to compute the swept volume of the manipulator given a reachable set of states; this enables one to guarantee safety by checking that the swept volume does not intersect with obstacles. The proposed method is compared to state-of-the-art methods and demonstrated on a variety of challenging manipulation examples in simulation, such as maneuvering a heavy dumbbell with uncertain mass around obstacles.

Method

A visualization of how the polynomial zonotope trajectory representation is used to construct the polynomial zonotope forward occupancy for a two link arm in 2D. A desired trajectory for each joint is shown in black in the top two rows. The same desired trajectory is depicted in each column. The planning time horizon is represented as a finite set of polynomial zonotopes (Sec. VIII-A1). In each column, a single time interval is highlighted in the top two rows and the corresponding time instance is highlighted in the visualization in the bottom row. The top two rows of the first column depict a finite set of polynomial zonotopes generated by uniformly buffering a desired trajectory by the ultimate bound (Lem. 16). The bottom row of the first column depicts the forward occupancy of the robot over this entire set (Lem. 18). The second column depicts a family of desired trajectories that are overapproximated by a finite set of polynomial zonotopes and the corresponding forward occupancy of the robot over this entire set. The third column depicts a family of desired trajectories buffered by the ultimate bound that are overapproximated by a finite set of polynomial zonotopes and the corresponding forward occupancy of the robot over this entire set. The fourth column depicts a subset of the sets illustrated in the third column generated by slicing in a specific trajectory parameter (Sec. VIII-A4). Note that the desired trajectory always remains within polynomial zonotopes.

Results

We evaluated ARMOUR on seven Hard Scenarios, with the start pose shown in white and the goal pose shown in black. There are seven tasks in the Hard Scenarios set: (1) from inside to outside of a box, (2-3) from one side of a wall to another, (4) between two horizontal posts, (5) from a sink to a cupboard, (6) from one set of shelves to another, (7) through a small window. (Please check the following videos in Chrome, Firefox or Edge)

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