Screw Geometry Meets Bandits: Incremental Acquisition of Demonstrations to Generate Manipulation Plans

TL;DR

An approach for the robot to incrementally and actively ask for new demonstration examples until the robot can assess with high confidence that it can perform the task successfully, using a screw geometric representation to generate manipulation plans from demonstrations.

Abstract

In this paper, we study the problem of methodically obtaining a sufficient set of kinesthetic demonstrations, one at a time, such that a robot can be confident of its ability to perform a complex manipulation task in a given region of its workspace. Although Learning from Demonstrations has been an active area of research, the problems of checking whether a set of demonstrations is sufficient, and systematically seeking additional demonstrations have remained open. We present a novel approach to address these open problems using (i) a screw geometric representation to generate manipulation plans from demonstrations, which makes the sufficiency of a set of demonstrations measurable; (ii) a sampling strategy based on PAC-learning from multi-armed bandit optimization to evaluate the robot's ability to generate manipulation plans in a subregion of its task space; and (iii) a heuristic to seek additional demonstration from areas of weakness. Thus, we present an approach for the robot to incrementally and actively ask for new demonstration examples until the robot can assess with high confidence that it can perform the task successfully. We present experimental results on two example manipulation tasks, namely, pouring and scooping, to illustrate our approach. A short video on the method: https://youtu.be/R-qICICdEos

Figures (6)

• Figure 1: Schematic sketch of a robot working in a table-top environment. The work area is indicated by the dashed rectangle.
• Figure 2: Overview of the motion segmentation algorithm mahalingam2023human for scooping the contents from a bowl using a spoon. Left: The human-provided demonstration is shown as a sequence of poses (of the spoon) in $SE(3)$, along with the pose of the bowl. Right: Segmenting the sequence of poses in $SE(3)$ into a sequence of guiding poses. Each pair of consecutive guiding poses forms a constant screw segment. The task-relevant constraints are the sequence of constant screw segments in a region of interest surrounding the task-related object, bowl.
• Figure 3: Snapshots of kinesthetic demonstrations of pouring (Fig: \ref{['fig:pouring-demo']}) and scooping (Fig: \ref{['fig:scooping-demo']}) tasks. In each demonstration, the left frame is the initial pose and the right one is the final pose.
• Figure 4: Visualization of the robot's change of belief about its ability to successfully perform tasks in the work area as it acquires demonstrations. The annotated black dots are the object locations during the demonstrations. The green and red dots are task instances for which plan generation succeeded and failed, respectively.
• Figure 5: Distribution (p.m.f) of demonstrations for different values of the number of regions $K$. For each $K$, the Self Evaluation algorithm (Alg. \ref{['alg:self-evaluation']}) was executed $1000$ times.

Theorems & Definitions (7)

• Definition 1: Coverage
• Definition 2: Sufficiency
• Theorem 1
• proof
• Theorem 2
• proof
• Corollary 2.1