Path planning with loop closure constraints using an atlas-based RRT

In many relevant path planning problems, loop closure constraints reduce the configuration space to a manifold embedded in the higher-dimensional joint ambient space. Whereas many progresses have been done to solve path planning problems in the presence of obstacles, only few work consider loop closure constraints. In this paper we present the AtlasRRT algorithm, a planner specially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize manifolds and to coordinate them forming an atlas. AtlasRRT simultaneously builds an atlas and a Rapidly-Exploring Random Tree (RRT), using the atlas to sample relevant configurations for the RRT, and the RRT to devise directions of expansion for the atlas. The new planner is advantageous since samples obtained from the atlas allow a more efficient extension of the RRT than state of the art approaches, where samples are generated in the joint ambient space.Peer ReviewedPostprint (author’s final draft

Path planning on manifolds using randomized higher-dimensional continuation

Despite the significant advances in path planning methods, problems involving highly constrained spaces are still challenging. In particular, in many situations the configuration space is a non-parametrizable variety implicitly defined by constraints, which complicates the successful generalization of sampling-based path planners. In this paper, we present a new path planning algorithm specially tailored for highly constrained systems. It builds on recently developed tools for Higher-dimensional Continuation, which provide numerical procedures to describe an implicitly defined variety using a set of local charts. We propose to extend these methods to obtain an efficient path planner on varieties, handling highly constrained problems. The advantage of this planner comes from that it directly operates into the configuration space and not into the higher-dimensional ambient space, as most of the existing methods do.Postprint (author’s final draft

EG-RRT: Environment-guided random trees for kinodynamic motion planning with uncertainty and obstacles

Existing sampling-based robot motion planning methods are often inefficient at finding trajectories for kinodynamic systems, especially in the presence of narrow passages between obstacles and uncertainty in control and sensing. To address this, we propose EG-RRT, an Environment-Guided variant of RRT designed for kinodynamic robot systems that combines elements from several prior approaches and may incorporate a cost model based on the LQG-MP framework to estimate the probability of collision under uncertainty in control and sensing. We compare the performance of EG-RRT with several prior approaches on challenging sample problems. Results suggest that EG-RRT offers significant improvements in performance.Postprint (author’s final draft

Exploring the energy landscapes of flexible molecular loops using higher-dimensional continuation

The conformational space of a flexible molecular loop includes the set of conformations fulfilling the geometric loop-closure constraints and its energy landscape can be seen as a scalar field defined on this implicit set. Higher-dimensional continuation tools, recently developed in Dynamical Systems and also applied to Robotics, provide efficient algorithms to trace out implicitly defined sets. This paper describes these tools and applies them to obtain full descriptions of the energy landscapes of short molecular loops that, otherwise, can only be partially explored, mainly via sampling. Moreover, to deal with larger loops, this paper exploits the higher-dimensional continuation tools to find local minima and minimum energy transition paths between them, without deviating from the loop-closure constraints. The proposed techniques are applied to previously studied molecules revealing the intricate structure of their energy landscapes

Path planning under kinematic constraints by rapidly exploring manifolds

The situation arising in path planning under kinematic constraints, where the valid configurations define a manifold embedded in the joint ambient space, can be seen as a limit case of the well-known narrow corridor problem. With kinematic constraints, the probability of obtaining a valid configuration by sampling in the joint ambient space is not low but null, which complicates the direct application of sampling-based path planners. This paper presents the AtlasRRT algorithm, which is a planner especially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize a manifold and to coordinate the charts, forming an atlas that fully covers it. AtlasRRT simultaneously builds an atlas and a bidirectional rapidly exploring random tree (RRT), using the atlas to sample configurations and to grow the branches of the RRTs, and the RRTs to devise directions of expansion for the atlas. The efficiency of AtlasRRT is evaluated in several benchmarks involving high-dimensional manifolds embedded in large ambient spaces. The results show that the combined use of the atlas and the RRTs produces a more rapid exploration of the configuration space manifolds than existing approaches.Peer Reviewe

Asymptotically-optimal path planning on manifolds

This paper presents an approach for optimal path planning on implicitly-defined configuration spaces such as those arising, for instance, when manipulating an object with two arms or with a multifingered hand. In this kind of situations, the kinematic and contact constraints induce configuration spaces that are manifolds embedded in higher dimensional ambient spaces. Existing sampling-based approaches for path planning on manifolds focus on finding a feasible solution, but they do not optimize the quality of the path in any sense. Thus, the returned paths are usually not suitable for direct execution. Recently, RRT* and other similar asymptotically-optimal path planners have been proposed to generate high-quality paths in the case of globally parametrizable configuration spaces. In this paper, we propose to use higher dimensional continuation tools to extend RRT* to the case of implicitly-defined configuration spaces. Experiments in different problems validate the proposed approach.Peer Reviewe

Efficient asymptotically-optimal path planning on manifolds

This paper presents an efficient approach for asymptotically-optimal path planning on implicitly-defined configuration spaces. Recently, several asymptotically-optimal path planners have been introduced, but they typically exhibit slow convergence rates. Moreover, these planners can not operate on the configuration spaces that appear in the presence of kinematic or contact constraints, such as when manipulating an object with two arms or with a multifingered hand. In these cases, the configuration space usually becomes an implicit manifold embedded in a higher-dimensional joint ambient space. Existing sampling-based path planners on manifolds focus on finding a feasible solution, but they do not optimize the quality of the path in any sense and, thus, the returned solution is usually not adequate for direct execution. In this paper, we adapt several techniques to accelerate the convergence of the asymptotically-optimal planners and we use higher-dimensional continuation tools to deal with the case of implicitly-defined configuration spaces. The performance of the proposed approach is evaluated through various experiments.Award-winnin

Path planning on manifolds using randomized higher-dimensional continuation

Despite the significant advances in path planning methods, problems involving highly constrained spaces are still challenging. In particular, in many situations the configuration space is a non-parametrizable variety implicitly defined by constraints, which complicates the successful generalization of sampling-based path planners. In this paper, we present a new path planning algorithm specially tailored for highly constrained systems. It builds on recently developed tools for Higher-dimensional Continuation, which provide numerical procedures to describe an implicitly defined variety using a set of local charts. We propose to extend these methods to obtain an efficient path planner on varieties, handling highly constrained problems. The advantage of this planner comes from that it directly operates into the configuration space and not into the higher-dimensional ambient space, as most of the existing methods do

Sampling-based path planning on configuration-space costmaps

This paper addresses path planning to consider a cost function defined over the configuration space. The proposed planner computes low-cost paths that follow valleys and saddle points of the configuration-space costmap. It combines the exploratory strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states. The planner is analyzed and shown to compute low-cost solutions with respect to a path-quality criterion based on the notion of mechanical work. A large set of experimental results is provided to demonstrate the effectiveness of the method. Current limitations and possible extensions are also discussed