Asymptotically Optimal Motion Planning for Learned Tasks Using Time-Dependent Cost Maps

Abstract

In unstructured environments in people’s homes and workspaces, robots executing a task may need to avoid obstacles while satisfying task motion constraints, e.g., keeping a plate of food level to avoid spills or properly orienting a finger to push a button. We introduce a sampling-based method for computing motion plans that are collision-free and minimize a cost metric that encodes task motion constraints. Our time-dependent cost metric, learned from a set of demonstrations, encodes features of a task’s motion that are consistent across the demonstrations and, hence, are likely required to successfully execute the task. Our sampling-based motion planner uses the learned cost metric to compute plans that simultaneously avoid obstacles and satisfy task constraints. The motion planner is asymptotically optimal and minimizes the Mahalanobis distance between the planned trajectory and the distribution of demonstrations in a feature space parameterized by the locations of task-relevant objects. The motion planner also leverages the distribution of the demonstrations to significantly reduce plan computation time. We demonstrate the method’s effectiveness and speed using a small humanoid robot performing tasks requiring both obstacle avoidance and satisfaction of learned task constraints. Note to Practitioners Motivated by the desire to enable robots to autonomously operate in cluttered home and workplace environments, this paper presents an approach for intuitively training a robot in a manner that enables it to repeat the task in novel scenarios and in the presence of unforeseen obstacles in the environment. Based on user-provided demonstrations of the task, our method learns features of the task that are consistent across the demonstrations and that we expect should be repeated by the robot when performing the task. We next present an efficient algorithm for planning robot motions to perform the task based on the learned features while avoiding obstacles. We demonstrate the effectiveness of our motion planner for scenarios requiring transferring a powder and pushing a button in environments with obstacles, and we plan to extend our results to more complex tasks in the future.

Asymptotically Optimal Motion Planning for Tasks Using Learned Virtual Landmarks

“…In [1], we presented an approach based on a user-specified feature space which incorporated the position of a landmark on the robot's end-effector (or grasped object) relative to landmarks in the environment. We extend that approach with the addition of learned time-invariant parameters on which the feature space is parameterized to reduce the amount of humanprovided information required.…”

“…Successfully performing this task requires properly positioning and orienting the pitcher relative the bowl, and this relative position and orientation changes over time during the the task (i.e., the pitcher's orientation is initially level and then changes so that the liquid pours out). Implicit in performing this example task is that the robot must be aware of certain task-relevant landmarks, including (1) awareness that the bowl (rather than other landmarks in the scene, e.g., the paper towel roll) is important to the task, and (2) awareness that the position of the spout of the pitcher (as apposed to other landmarks on the pitcher) is most important to successfully pouring the liquid into the bowl. Utilizing appropriate task-relevant landmarks is often critical to successfully performing a task.…”

“…existing approach for motion planning for a learned task [1], [2]. Prior approaches for learning manipulation tasks often assume that task-relevant landmarks are manually specified by a user (e.g., [1]- [5]).…”

“…Prior approaches for learning manipulation tasks often assume that task-relevant landmarks are manually specified by a user (e.g., [1]- [5]). Our new method for automatically learning task-relevant landmarks (e.g., selecting the bowl and pitcher's spout in the scenario in Fig.…”

“…Following the general approach of learning from demonstrations, during a learning phase a user provides a set of kinesthetic demonstrations of a task. In our implementation, we learn a task model that can be used in conjunction with a samplingbased motion planner [1]. To execute the learned task in a new environment where task-relevant objects may have moved, we execute an asymptotically optimal sampling-based motion planner that plans a trajectory that maximally adheres to the learned task model while avoiding obstacles.…”