Simplex-Tree Based Kinematics of Foldable Objects as Multi-body Systems Involving Loops

Springer Tracts in Advanced Robotics

2009

Motion planning for spatially constrained robots is difficult due to additional constraints placed on the robot, such as closure constraints for closed chains or requirements on end effector placement for articulated linkages. It is usually computationally too expensive to apply sampling-based planners to these problems since it is difficult to generate valid configurations. We overcome this challenge by redefining the robot's degrees of freedom and constraints into a new set of parameters, called reachable distance space (RD-space), in which all configurations lie in the set of constraint-satisfying subspaces. This enables us to directly sample the constrained subspaces with complexity linear in the robot's complexity. In addition to supporting efficient sampling of configurations, we show that the RD-space formulation naturally supports planning, and in particular, we design a local planner suitable for use by sampling-based planners. We demonstrate the effectiveness and efficiency of our approach for spatially constrained systems including closed chain planning with multiple loops, restricted end effector sampling, and on-line planning for drawing (or sculpting).

Section: Related Workmentioning

confidence: 87%

Section: Application: Closed Chain Planningmentioning

confidence: 99%

Planning with Reachable Distances

Tang

Springer Tracts in Advanced Robotics

2009

“…Han et al (2006) solved closed-chain problems by transforming them into a system of linear inequalities. Extensions are capable of solving closed-chain problems with multiple loops (Han and Rudolph, 2009). This method is able to handle problems with thousands of links or thousands of loops.…”

Section: Related Workmentioning

confidence: 99%

Sampling-based motion planning with reachable volumes for high-degree-of-freedom manipulators

McMahon

The International Journal of Robotics Research

2018

Motion planning for constrained systems is a version of the motion planning problem in which the motion of a robot is limited by constraints. For example, one can require that a humanoid robot such as a PR2 remain upright by constraining its torso to be above its base or require that an object such as a bucket of water remain upright by constraining the vertices of the object to be parallel to the robot's base. Grasping can be modeled by requiring that the end effectors of the robot be located at specified handle positions. Constraints might require that the robot remain in contact with a surface, or that certain joints of the robot remain in contact with each other (e.g., closed chains). Such problems are particularly difficult because the constraints form a manifold in C-space, and planning must be restricted to this manifold. High-degree-offreedom motion planning and motion planning for constrained systems has applications in parallel robotics, grasping and manipulation, computational biology and molecular simulations, and animation. We introduce a new concept, reachable volumes, that are a geometric representation of the regions the joints and end effectors of a robot can reach, and use it to define a new planning space called RV-space where all points automatically satisfy a problem's constraints. Visualizations of reachable volumes can enable operators to see the regions of workspace that different parts of the robot can reach. Samples and paths generated in RV-space naturally conform to constraints, making planning for constrained systems no more difficult than planning for unconstrained systems. Consequently, constrained motion planning problems that were previously difficult or unsolvable become manageable and in many cases trivial. We introduce tools and techniques to extend the state-of-the-art sampling-based motion planning algorithms to RV-space. We define a reachable volumes sampler, a reachable volumes local planner, and a reachable volumes distance metric. We showcase the effectiveness of RV-space by applying these tools to motion planning problems for robots with constraints on the end effectors and/or internal joints of the robot. We show that RV-based planners are more efficient than existing methods, particularly for higher-dimensional problems, solving problems with 1000 or more degrees of freedom for multi-loop and tree-like linkages.

“…solve closed chain problems by transforming them into a system of linear inequalities [9]. Extensions are capable of solving closed chain problems with multiple loops [13]. This method is able to handle problems with thousands of links or thousands of loops.…”

Section: Enforcing Constraints During Samplingmentioning

confidence: 99%

Sampling based motion planning with reachable volumes: Application to manipulators and closed chain systems

McMahon

2014 IEEE/RSJ International Conference on Intelligent Robots and Systems

2014

We introduce a new concept, reachable volumes, which denotes the set of points that the end effector of a chain or linkage can reach. This generalizes work on reachable distances for planar robots to 3-dimensional spherical joints. We show that the reachable volume of a chain is equivalent to the Minkowski sum of the reachable volumes of its links, which gives us an efficient method for computing reachable volumes. We present a method for generating configurations using reachable volumes for various types of robots including chain robots (with and without closure constraints), tree-like robots, and robots containing a combination of them. Unlike previous methods, ours works for 3-dimensional linkages with spherical joints and is capable of generating samples for problems with constraints on internal joints as well as end effectors. We show that reachable volumes samples are less likely to be invalid due to self-collisions, making reachable volumes sampling more efficient for higher dimensional problems. We also show that these samples are easier to connect than others, resulting in more connected roadmaps. Finally we demonstrate that our method can be applied to 262-dof, multi-loop, and tree-like linkages, problems where existing methods cannot be used (e.g., closed chains with spherical joints) or cannot be solved efficiently (e.g., tree-like robots and high degree of freedom chains with spherical joints).