Sampling-based optimal kinodynamic planning with motion primitives

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree {of feasible trajectories in the RRT* by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity

A randomized kinodynamic planner for closed-chain robotic systems

Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin

An Extensible Benchmarking Infrastructure for Motion Planning Algorithms

Sampling-based planning algorithms are the most common probabilistically complete algorithms and are widely used on many robot platforms. Within this class of algorithms, many variants have been proposed over the last 20 years, yet there is still no characterization of which algorithms are well-suited for which classes of problems. This has motivated us to develop a benchmarking infrastructure for motion planning algorithms. It consists of three main components. First, we have created an extensive benchmarking software framework that is included with the Open Motion Planning Library (OMPL), a C++ library that contains implementations of many sampling-based algorithms. Second, we have defined extensible formats for storing benchmark results. The formats are fairly straightforward so that other planning libraries could easily produce compatible output. Finally, we have created an interactive, versatile visualization tool for compact presentation of collected benchmark data. The tool and underlying database facilitate the analysis of performance across benchmark problems and planners.Comment: Submitted to IEEE Robotics & Automation Magazine (Special Issue on Replicable and Measurable Robotics Research), 201