Motion Planning of Nonholonomic Cooperative Mobile Manipulators

TL;DR

The paper addresses real-time kinodynamic motion planning for cooperative nonholonomic mobile manipulators transporting an object in environments with static and dynamic obstacles. It advances a two-stage framework combining offline visibility-vertices path planning to produce a global path $S$ with surrounding convex polygons and an online NMPC-based planner that jointly optimizes the base and arm motions within kinodynamic and collision constraints, guided by a time-normalized Bezier reference $p_r(c_t)$. Key contributions include the visibility-vertices offline path planner for nonconvex obstacles, ellipse-based convexification to form convex polygons around path segments, and a CasADi/Ipopt-based online planner enforcing static/dynamic obstacle avoidance, self-collision, and grasp constraints for nonholonomic MMRs. The results from simulations and hardware demonstrations show real-time performance and robust obstacle avoidance, with future work aimed at smoothing trajectories near obstacle-free polytope intersections and potential speedups via a C++ implementation.

Abstract

We propose a real-time implementable motion planning technique for cooperative object transportation by nonholonomic mobile manipulator robots (MMRs) in an environment with static and dynamic obstacles. The proposed motion planning technique works in two steps. A novel visibility vertices-based path planning algorithm computes a global piece-wise linear path between the start and the goal location in the presence of static obstacles offline. It defines the static obstacle free space around the path with a set of convex polygons for the online motion planner. We employ a Nonliner Model Predictive Control (NMPC) based online motion planning technique for nonholonomic MMRs that jointly plans for the mobile base and the manipulators arm. It efficiently utilizes the locomotion capability of the mobile base and the manipulation capability of the arm. The motion planner plans feasible motion for the MMRs and generates trajectory for object transportation considering the kinodynamic constraints and the static and dynamic obstacles. The efficiency of our approach is validated by numerical simulation and hardware experiments in varied environments.

Figures (13)

• Figure 1: Formation of five non-holonomic MMRs holding an object. The MMRs grasped the object to transport collaboratively from one place to another.
• Figure 2: Two step motion planning process: offline path planning and online motion planning.
• Figure 3: Offline path planning process.
• Figure 4: Path Polygon for $S_2$ computed using the visible vertices of $W_2$ and $W_3$.
• Figure 5: The polygon convexification process step by step. For the path segment 2 in Fig. \ref{['fig:5a']}, an ellipse touching the nearest concave vertex of the polygon has been formed and a tangent (red line) to the ellipse at this point has been drawn. The tangent cuts the polygon bounded by black edges and the polygon (sky blue) containing the path segment has been kept. The ellipse has been dilated keeping the aspect ratio same in Fig \ref{['fig:5b']} till it touches the nearest concave vertex of the new polygon. Here a very small portion of the polygon is cut by the tangent to the ellipse at this concave vertex. The process continues till any concave vertex remains and a convex polygon is formed (green polygon in Fig. \ref{['fig:5d']}.)