Collaborative Robotic Motion Planning

When attempting to plan for an interaction between two robots there are many factors that compound its complexity, including the number of joints each robot has, causes for collision, power usage, placement of the end effectors, and others. These factors compound themselves as the robots involved increase in joints, there is an increase in obstacles, or more robots are added to the system. In an effort to devise an algorithm that provides a fast and effective solution to these types of problems, previous work has been done on Reachable Volumes and Interaction Templates, algorithms that serve to reduce the processing time for high degrees-of-freedom (dof) robots with stringent constraints, and to reduce the processing time for certain interactions between two or more systems of robots, respectively. Reachable Volumes uses the volumes that each joint of the robot can occupy, and by choosing points within these volumes it can solve for a configuration at a given end effector position. This enables a quick way to evaluate a configuration for a high dof robot as well as providing a means of avoiding collisions with obstacles by simply sampling the volumes around the joints in areas not occupied by the obstacles. Additionally, another strength of Reachable Volumes is it provides the ability to precisely place the end effector at a desired location, which other motion planning algorithms struggle with. Interaction Templates can be used to "template" or formulate an interaction such as a handoff that can be applied to a "roadmap" or a collection of points that make up the movements of a manipulator in configuration space. In doing so, Interaction Templates can make complex and processing expensive tasks such as calculating for a handoff interaction much more efficient. The work below begins to integrate elements from the Reachable Volumes algorithm into Interaction Templates, which speeds up several steps on the Interaction Templates Algorithm as well as makes it more effective for high dof robots or situations with a multitude of constraints. It additionally sets up a framework for more robots to be included in the algorithm

Managing Temporal Robot Constraints using Reachable Volumes

This project focuses on planning the motion for high degree of freedom manipulator robots under dynamic (or temporal) constraints. Manipulator robots are widely used in industry and are important because they can do jobs that are either too tedious or too dangerous for humans. An example would be picking up toxic waste or exploring underwater archeological sites. Motion planning for high degree of freedom (DOF) manipulators under task constraints is challenging because it gives rise to high dimensional configuration spaces (C-space) that are complex in structure. Our approach reduces the complexity by re-parameterizing the manipulator robots DOFs into a space that contains the valid regions that the end effector of the robot can reach, known as the Reachable Volume space (RV-space). In this way, we can sample valid configurations in Cspace in linear time with the number of DOFs of the manipulator. Current Reachable Volume theory only handles permanent constraints and cannot adapt to scenarios that require constraints that are enabled at certain times in the problem and disabled at other times. For example, when a manipulator grabs an object, closure constraints on the grasper must be satisfied, but when the object is to be dropped, these constraints must be ignored. Additionally, certain scenarios require the cooperation of multiple robots. This is obvious if we consider problems that involve objects that are too large for a single robot to handle. In this work, we produce a working computational framework for efficient motion planning of high degree of freedom manipulator arms under dynamic constraints through the extension of existing work in Reachable Volume spaces

Managing Temporal Robot Constraints using Reachable Volumes

This project focuses on planning the motion for high degree of freedom manipulator robots under dynamic (or temporal) constraints. Manipulator robots are widely used in industry and are important because they can do jobs that are either too tedious or too dangerous for humans. An example would be picking up toxic waste or exploring underwater archeological sites. Motion planning for high degree of freedom (DOF) manipulators under task constraints is challenging because it gives rise to high dimensional configuration spaces (C-space) that are complex in structure. Our approach reduces the complexity by re-parameterizing the manipulator robots DOFs into a space that contains the valid regions that the end effector of the robot can reach, known as the Reachable Volume space (RV-space). In this way, we can sample valid configurations in Cspace in linear time with the number of DOFs of the manipulator. Current Reachable Volume theory only handles permanent constraints and cannot adapt to scenarios that require constraints that are enabled at certain times in the problem and disabled at other times. For example, when a manipulator grabs an object, closure constraints on the grasper must be satisfied, but when the object is to be dropped, these constraints must be ignored. Additionally, certain scenarios require the cooperation of multiple robots. This is obvious if we consider problems that involve objects that are too large for a single robot to handle. In this work, we produce a working computational framework for efficient motion planning of high degree of freedom manipulator arms under dynamic constraints through the extension of existing work in Reachable Volume spaces

Design and control of kinematically redundant robots for maximizing failure-tolerant workspaces

2021 Spring.Includes bibliographical references.Kinematically redundant robots have extra degrees of freedom so that they can tolerate a joint failure and still complete an assigned task. Previous work has defined the "failure-tolerant workspace" as the workspace that is guaranteed to be reachable both before and after an arbitrary locked-joint failure. One mechanism for maximizing this workspace is to employ optimal artificial joint limits prior to a failure. This dissertation presents two techniques for determining these optimal artificial joint limits. The first technique is based on the gradient ascent method. The proposed technique is able to deal with the discontinuities of the gradient that are due to changes in the boundaries of the failure tolerant workspace. This technique is illustrated using two examples of three degree-of-freedom planar serial robots. The first example is an equal link length robot where the optimal artificial joint limits are computed exactly. In the second example, both the link lengths and artificial joint limits are determined, resulting in a robot design that has more than twice the failure-tolerant area of previously published locally optimal designs. The second technique presented in this dissertation is a novel hybrid technique for estimating the failure-tolerant workspace size for robots of arbitrary kinematic structure and any number of degrees of freedom performing tasks in a 6D workspace. The method presented combines an algorithm for computing self-motion manifold ranges to estimate workspace envelopes and Monte-Carlo integration to estimate orientation volumes to create a computationally efficient algorithm. This algorithm is then combined with the coordinate ascent optimization technique to determine optimal artificial joint limits that maximize the size of the failure-tolerant workspace of a given robot. This approach is illustrated on multiple examples of robots that perform tasks in 3D planar and 6D spatial workspaces

Motion Primitives and Planning for Robots with Closed Chain Systems and Changing Topologies

When operating in human environments, a robot should use predictable motions that allow humans to trust and anticipate its behavior. Heuristic search-based planning offers predictable motions and guarantees on completeness and sub-optimality of solutions. While search-based planning on motion primitive-based (lattice-based) graphs has been used extensively in navigation, application to high-dimensional state-spaces has, until recently, been thought impractical. This dissertation presents methods we have developed for applying these graphs to mobile manipulation, specifically for systems which contain closed chains. The formation of closed chains in tasks that involve contacts with the environment may reduce the number of available degrees-of-freedom but adds complexity in terms of constraints in the high-dimensional state-space. We exploit the dimensionality reduction inherent in closed kinematic chains to get efficient search-based planning. Our planner handles changing topologies (switching between open and closed-chains) in a single plan, including what transitions to include and when to include them. Thus, we can leverage existing results for search-based planning for open chains, combining open and closed chain manipulation planning into one framework. Proofs regarding the framework are introduced for the application to graph-search and its theoretical guarantees of optimality. The dimensionality-reduction is done in a manner that enables finding optimal solutions to low-dimensional problems which map to correspondingly optimal full-dimensional solutions. We apply this framework to planning for opening and navigating through non-spring and spring-loaded doors using a Willow Garage PR2. The framework motivates our approaches to the Atlas humanoid robot from Boston Dynamics for both stationary manipulation and quasi-static walking, as a closed chain is formed when both feet are on the ground

Constrained Bimanual Planning with Analytic Inverse Kinematics

In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality constraints in the configuration space, which are difficult for trajectory optimizers. In addition, the set of feasible configurations becomes a measure zero set, which presents a challenge to sampling-based motion planners. We leverage an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure. We describe how to use this parametrization with existing algorithms for motion planning, including sampling-based approaches, trajectory optimizers, and techniques that plan through convex inner-approximations of collision-free space.Comment: Submitted to ICRA 2024. 8 pages, 5 figures. Interactive results available at https://cohnt.github.io/Bimanual-Web/index.htm