Unifying configuration space and sensor space for vision-based motion planning

A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning algorithms and reveals how the topology of the robot's configuration space influences their structure. We prove that the topological complexity of motion planning TC(X) coincides with the minimal n such that there exists an n-valued random motion planning algorithm for the system; here $X$ denotes the configuration space. We study in detail the problem of collision free motion of several objects on a graph G. We describe an explicit motion planning algorithm for this problem. We prove that if G is a tree and if the number of objects is large enough, then the topological complexity of this motion planning problem equals 2m(G)+1 where m(G) is the number of the essential vertices of G. It turns out (in contrast with the results on the collision free control of many objects in space obtained earlier jointly with S. Yuzvinsky) that the topological complexity is independent of the number of particles.

Recent progress in motion planning has made it possible to determine homotopy inequivalent trajectories between an initial and terminal configuration in a robot configuration space. Current approaches have however either assumed the knowledge of differential one-forms related to a skeletonization of the collision space, or have relied on a simplicial representation of the free space. Both of these approaches are currently however not yet practical for higher dimensional configuration spaces. We propose 2D topological task projections (TTPs): mappings from the configuration space to 2-dimensional spaces where simplicial complex filtrations and persistent homology can identify topological properties of the high-dimensional free configuration space. Our approach only requires the availability of collision free samples to identify winding centers that can be used to determine homotopy inequivalent trajectories. We propose the Winding Augmented RRT and RRT* (WA-RRT/RRT*) algorithms using which homotopy inequivalent trajectories can be found. We evaluate our approach in experiments with configuration spaces of planar linkages with 2–10 degrees of freedom. Results indicate that our approach can reliably identify suitable topological task projections and our proposed WA-RRT and WA-RRT* algorithms were able to identify a collection of homotopy inequivalent trajectories in each considered configuration space dimension.

Traditional motion planning can be computationally burdensome for practical robots, due to extensive collision checking and considerable iterative propagation of cost values. We present a novel neural network architecture which can directly generate the cost-to-go (c2g) function for a given configuration space and a goal configuration. The output of the network is a continuous function whose gradient in configuration space can be directly used to generate trajectories in motion planning without the need for protracted iterations or extensive collision checking. This higher order function (i.e. a function generating another function) representation lies at the core of our motion planning architecture, c2g-HOF, which can take a workspace as input, and generate the cost-to-go function over the configuration space map (C-map). Simulation results for 2D and 3D environments show that c2g-HOF can be orders of magnitude faster at execution time than methods which explore the configuration space during execution. We also present an implementation of c2g-HOF which generates trajectories for robot manipulators directly from an overhead image of the workspace.

Whole-body motion and footstep planning for humanoid robots with multi-heuristic search

Motion planning for robotic manipulation of clothing is a challenging problem as clothing articles have high-dimensional configuration spaces and are computationally expensive to simulate. We present an algorithm for robotic cloth folding that, given a sequence of desired folds, outputs a motion plan consisting of a sequence of primitives for a robot to fold the cloth. Previous work on cloth folding does not take into account the constraints of the robot, and thus produces plans which are often infeasible given the kinematics of robots like the Willow Garage PR2. In this paper we introduce a class of motion primitives that start and end in a subset of the cloth’s state space. To find a sequence of primitives that achieves all required folds, the algorithm takes advantage of the partial ordering inherent in folding, and produces a time-optimal motion plan (given the set of primitives) for the robot if one exists. We describe experiments with a general purpose mobile robotic platform, the PR2, folding articles that require dragging and base motion in addition to folding. Our experiments show that (1) many articles of clothing conform well enough to the assumptions made in our model and (2) this approach allows our robot to perform a wide variety of folds on articles of various sizes and shapes.

We study the problem of generating motion plans for kinematically controllable underactuated systems in environments cluttered with obstacles. We develop a computationally efficient motion planning algorithm that finds fast trajectories by exploiting closed-form inverse kinematics of the robot. The completeness property of the motion planning algorithm can be proven using appropriate metrics defined in the configuration space of the kinematically controllable systems. The snakeboard is used as an example of a kinematically controllable underactuated system to test the motion planning algorithm, and motion plans have been implemented on an experimental snakeboard.

This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High-dimensionality of the robot configuration space often leads to difficulties in utilizing the widely-used motion planning algorithms, since the volume of the decision space increases exponentially with the number of dimensions. To handle complications arising from the large decision space, and to solve a corresponding motion planning problem efficiently, two key concepts are adopted in this work: First, the Gaussian process latent variable model (GP-LVM) is utilized for low-dimensional representation of the original configuration space. Second, an approximate inference algorithm is used, exploiting through the duality between control and estimation, to explore the decision space and to compute a high-quality motion trajectory of the robot. Utilizing the GP-LVM and the duality between control and estimation, we construct a fully probabilistic generative model with which a high-dimensional motion planning problem is transformed into a tractable inference problem. Finally, we compute the motion trajectory via an approximate inference algorithm based on a variant of the particle filter. The resulting motions can be viewed in the supplemental video. ( https://youtu.be/kngEaOR4Esc )

We propose a new approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. It is inspired by recent motion planning research and explicitly takes into account constraints due to joint limits and self-collisions. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the configuration space of a manipulator in a finite graph like structure. The standard formulation of inverse kinematics problem is then solved using this roadmap. Our current implementation, based on Ariadne's clew algorithm, is composed of two sub-algorithms: EXPLORE, a simple algorithm that builds the kinematic roadmap by placing landmarks in the configuration space; and SEARCH, a local planner that uses this roadmap to reach the desired end-effector configuration. Our implementation of SEARCH is an extremely efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.

Task and Motion Planning for Apple Harvesting Robot

Path planning has been widely studied by computer scientists. However, it is a very simplified version of the motion planning problems occurring in robotics. This paper examines extensions yielding two important issues: controllability and recognizability. The controllability issue arises when the number of controls is smaller than the number of independent parameters defining the robot's configuration: Can the motions span the configuration space? The recognizability issue occurs when there are errors in control and sensing: Can the robot recognize goal achievement? Both issues have interesting impact on the computational complexity of motion planning. This paper will also discuss a new path planning scheme based on random sampling of configuration space, to deal with many-degree-of-freedom robots. The blend of controllability, recognizability, and complexity issues discussed in this paper is unique to robotics and its study is key to the development of autonomous robots.

Chapter 18 - Distances in Mathematical Engineering

A modified magnetic field (MMF) has been used for the generation of robot motion plans of a linked manipulator such as a robot arm, in a complex workspace while veering around enclosing obstacle walls. The MMF method ensures global convergence and collision constraint satisfaction while allowing the application of this method as an online plan generation and control technique in both Cartesian and configuration spaces. Methods for using the MMF to perform both the planning and dynamic control of a robot arm around obstacles and singular configurations are developed in this paper and results shown for a specific workspace configuration.

To reduce the computational cost of humanoid motion generation, we introduce a new approach to representing robot kinematic reachability: the differentiable reachability map. This map is a scalar-valued function defined in the task space that takes positive values only in regions reachable by the robot's end-effector. A key feature of this representation is that it is continuous and differentiable with respect to task-space coordinates, enabling its direct use as constraints in continuous optimization for humanoid motion planning. We describe a method to learn such differentiable reachability maps from a set of end-effector poses generated using a robot's kinematic model, using either a neural network or a support vector machine as the learning model. By incorporating the learned reachability map as a constraint, we formulate humanoid motion generation as a continuous optimization problem. We demonstrate that the proposed approach efficiently solves various motion planning problems, including footstep planning, multi-contact motion planning, and loco-manipulation planning for humanoid robots.

In this paper, we propose a mission aware motion planning (MAP) framework for a swarm of autonomous unmanned ground vehicles (UGVs) or mobile stations in an uncertain environment for efficient supply of resources/services to unmanned aerial vehicles (UAVs) performing a specific mission. The MAP framework consists of two levels, namely, centralized mission planning and decentralized motion planning. On the first level, the centralized mission planning algorithm estimates the density of UAV in a given environment for determining the number of UGVs and their initial operating location. In the subsequent level, a decentralized motion planning algorithm which provides a closed-form expression for velocity command using adaptive density estimation has been proposed. Further, the physical and geographical constraints are integrated into motion planning. A Monte-Carlo simulation is performed to evaluate the advantages of the MAP over distributed stationary stations (DSSs) often used in the literature. The obtained results clearly indicate that in comparison with DSS, MAP reduces the average distance traveled by UAVs about 20%, reduces the loss of mission time by 90 s per interruption and power loss by 3 dB.

Figure 2.1 shows a framework of motion control system including the trajectory generation. Motion Planning is sometimes called Trajectory Planning. Motion Planning is the function in order to decide how to move based on intent of an operator or decision of a robot. If a control system is the position control system, the information that Motion Planning output is the position information; if a control system is the force control system, the force information is given. In the following, we give explanation on the premise of the position control.