On the Synthesis of Reactive Collision-Free Whole-Body Robot Motions: A Complementarity-based Approach

This paper is about generating motion plans for high degree-of-freedom systems that account for collisions along the entire body. A particular class of mathematical programs with complementarity constraints become useful in this regard. Optimization-based planners can tackle confined-space trajectory planning while being cognizant of robot constraints. However, introducing obstacles in this setting transforms the formulation into a non-convex problem (oftentimes with ill-posed bilinear constraints), which is non-trivial in a real-time setting. To this end, we present the FLIQC (Fast LInear Quadratic Complementarity based) motion planner. Our planner employs a novel motion model that captures the entire rigid robot as well as the obstacle geometry and ensures non-penetration between the surfaces due to the imposed constraint. We perform thorough comparative studies with the state-of-the-art, which demonstrate improved performance. Extensive simulation and hardware experiments validate our claim of generating continuous and reactive motion plans at 1 kHz for modern collaborative robots with constant minimal parameters.

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

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

Provable Methods for Searching with an Imperfect Sensor

Assume that a target is known to be present at an unknown point among a finite set of locations in the plane. We search for it using a mobile robot that has imperfect sensing capabilities. It takes time for the robot to move between locations and search a location; we have a total time budget within which to conduct the search. We study the problem of computing a search path/strategy for the robot that maximizes the probability of detection of the target. Considering non-uniform travel times between points (e.g., based on the distance between them) is crucial for search and rescue applications; such problems have been investigated to a limited extent due to their inherent complexity. In this paper, we describe fast algorithms with performance guarantees for this search problem and some variants, complement them with complexity results, and perform experiments to observe their performance.

A General Formulation for Path Constrained Time-Optimized Trajectory Planning with Environmental and Object Contacts

A typical manipulation task consists of a manipulator equipped with a gripper to grasp and move an object with constraints on the motion of the hand-held object, which may be due to the nature of the task itself or from object-environment contacts. In this paper, we study the problem of computing joint torques and grasping forces for time-optimal motion of an object, while ensuring that the grasp is not lost and any constraints on the motion of the object, either due to dynamics, environment contact, or no-slip requirements, are also satisfied. We present a second-order cone program (SOCP) formulation of the time-optimal trajectory planning problem that considers nonlinear friction cone constraints at the hand-object and object-environment contacts. Since SOCPs are convex optimization problems that can be solved optimally in polynomial time using interior point methods, we can solve the trajectory optimization problem efficiently. We present simulation results on three examples, including a non-prehensile manipulation task, which shows the generality and effectiveness of our approach.

Containerized Vertical Farming Using Cobots

Containerized vertical farming is a type of vertical farming practice using hydroponics in which plants are grown in vertical layers within a mobile shipping container. Space limitations within shipping containers make the automation of different farming operations challenging. In this paper, we explore the use of cobots (i.e., collaborative robots) to automate two key farming operations, namely, the transplantation of saplings and the harvesting of grown plants. Our method uses a single demonstration from a farmer to extract the motion constraints associated with the tasks, namely, transplanting and harvesting, and can then generalize to different instances of the same task. For transplantation, the motion constraint arises during insertion of the sapling within the growing tube, whereas for harvesting, it arises during extraction from the growing tube. We present experimental results to show that using RGBD camera images (obtained from an eye-in-hand configuration) and one demonstration for each task, it is feasible to perform transplantation of saplings and harvesting of leafy greens using a cobot, without task-specific programming.

Task-Oriented Grasping with Point Cloud Representation of Objects

In this paper, we study the problem of task-oriented grasp synthesis from partial point cloud data using an eye-in-hand camera configuration. In task-oriented grasp synthesis, a grasp has to be selected so that the object is not lost during manipulation, and it is also ensured that adequate force/moment can be applied to perform the task. We formalize the notion of a gross manipulation task as a constant screw motion (or a sequence of constant screw motions) to be applied to the object after grasping. Using this notion of task, and a corresponding grasp quality metric developed in our prior work, we use a neural network to approximate a function for predicting the grasp quality metric on a cuboid shape. We show that by using a bounding box obtained from the partial point cloud of an object, and the grasp quality metric mentioned above, we can generate a good grasping region on the bounding box that can be used to compute an antipodal grasp on the actual object. Our algorithm does not use any manually labeled data or grasping simulator, thus making it very efficient to implement and integrate with screw linear interpolation-based motion planners. We present simulation as well as experimental results that show the effectiveness of our approach.

Human-Guided Planning for Complex Manipulation Tasks Using the Screw Geometry of Motion

In this paper, we present a novel method of motion planning for performing complex manipulation tasks by using human demonstration and exploiting the screw geometry of motion. We consider complex manipulation tasks where there are constraints on the motion of the end effector of the robot. Examples of such tasks include opening a door, opening a drawer, transferring granular material from one container to another with a spoon, and loading dishes to a dishwasher. Our approach consists of two steps: First, using the fact that a motion in the task space of the robot can be approximated by using a sequence of constant screw motions, we segment a human demonstration into a sequence of constant screw motions. Second, we use the segmented screws to generate motion plans via screw-linear interpolation for other instances of the same task. The use of screw segmentation allows us to capture the invariants of the demonstrations in a coordinate-free fashion, thus allowing us to plan for different task instances from just one example. We present extensive experimental results on a variety of manipulation scenarios showing that our method can be used across a wide range of manipulation tasks.

Coordinate Invariant User-Guided Constrained Path Planning with Reactive Rapidly Expanding Plane-Oriented Escaping Trees

As collaborative robots move closer to human environments, motion generation and reactive planning strategies that allow for elaborate task execution with minimal easy-to-implement guidance whilst coping with changes in the environment is of paramount importance. In this paper, we present a novel approach for generating real-time motion plans for point-to-point tasks using a single successful human demonstration. Our approach is based on screw linear interpolation,which allows us to respect the underlying geometric constraints that characterize the task and are implicitly present in the demonstration. We also integrate an original reactive collision avoidance approach with our planner. We present extensive experimental results to demonstrate that with our approach,by using a single demonstration of moving one block, we can generate motion plans for complex tasks like stacking multiple blocks (in a dynamic environment). Analogous generalization abilities are also shown for tasks like pouring and loading shelves. For the pouring task, we also show that a demonstration given for one-armed pouring can be used for planning pouring with a dual-armed manipulator of different kinematic structure.

Computing a Task-Dependent Grasp Metric Using Second Order Cone Programs

Evaluating a grasp generated by a set of hand-object contact locations is a key component of many grasp planning algorithms. In this paper, we present a novel second order cone program (SOCP) based optimization formulation for evaluating a grasps' ability to apply wrenches to generate a linear motion along a given direction and/or an angular motion about the given direction. Our quality measure can be computed efficiently, since the SOCP is a convex optimization problem, which can be solved optimally with interior point methods. A key feature of our approach is that we can consider the effect of contact wrenches from any contact of the object with the environment. This is different from the extant literature where only the effect of finger-object contacts is considered. Exploiting the environmental contact is useful in many manipulation scenarios either to enhance the dexterity of simple hands or improve the payload capability of the manipulator. In contrast to most existing approaches, our approach also takes into account the practical constraint that the maximum contact force that can be applied at a finger-object contact can be different for each contact. We can also include the effect of external forces like gravity, as well as the joint torque constraints of the fingers/manipulators. Furthermore, for a given motion path as a constant screw motion or a sequence of constant screw motions, we can discretize the path and compute a global grasp metric to accomplish the whole task with a chosen set of finger-object contact locations.

Task Space Planning with Complementarity Constraint-based Obstacle Avoidance

In this paper, we present a task space-based local motion planner that incorporates collision avoidance and constraints on end-effector motion during the execution of a task. Our key technical contribution is the development of a novel kinematic state evolution model of the robot where the collision avoidance is encoded as a complementarity constraint. We show that the kinematic state evolution with collision avoidance can be represented as a Linear Complementarity Problem (LCP). Using the LCP model along with Screw Linear Interpolation (ScLERP) in SE(3), we show that it may be possible to compute a path between two given task space poses by directly moving from the start to the goal pose, even if there are potential collisions with obstacles. The scalability of the planner is demonstrated with experiments using a physical robot. We present simulation and experimental results with both collision avoidance and task constraints to show the efficacy of our approach.