Obround trees: sparsity enhanced feedback motion planning of differential drive robotic systems

Abstract

Robot motion planning & control is one of the most critical and prevalent problems in the robotics community. Even though original motion planning algorithms had relied on "open-loop" strategies and policies, researchers and engineers have been focusing on feedback motion planning and control algorithms due to the uncertainties, such as process and sensor noise, of autonomous robotic applications. Recently, several studies proposed some robust feedback motion planning strategies based on sparsely connected safe zones. In this class of planning and control policies, local control policy inside a single zone computes and feeds the control actions that can drive the robot to a different connected region while guaranteeing that the robot never exceeds the boundaries of the active area until convergence. While most of these studies apply only to holonomic robotic models, a recent motion planning method (RCT) can solve the motion planning and navigation problems for unicycle like robotic systems based on a randomly connected circular region tree. In this paper, we propose a new/updated feedback motion planning algorithm that substantially enhances the sparsity, computational feasibility, and input effort compared to their methodology. The new algorithm generates a sparse neighborhood tree as a set of connected obround zones. Obround regions cover larger areas inside the environment, thus leads to a more sparse tree structure. During navigation, we modify the nonlinear control policy adopted in RCT method to handle the obround shaped zones. The feedback control policy navigates the robot model from one obround zone to the adjacent area in the tree structure, ensuring it stays inside the active region's boundaries and asymptotically reaches the connected obround. We demonstrate the effectiveness and validity of the algorithm on simulation studies. Our Monte Carlo simulations show that our enhancement to the original algorithm probabilistically improves the sparsity, and produces smoother trajectories compared to two motion planning algorithms that rely on sampling based neighborhood structures.

Cloud Hopping; Navigating in 3D Uneven Environments via Supervoxels and Control Lyapunov Function

“…Authors in [2] proposed a feedback motion strategy for a differential drive robot based on a network of obstacle-free regions, which is similar to our approach in terms of using a connectivity graph. First, within the environment, a graph or tree structure composed of safe zones (boxes, rectangles) is created.…”