From Obstacle-Based Space Partitioning to Corridors and Path Planning. A Convex Lifting Approach

Abstract

This paper proposes a novel methodology for path generation in known and congested multi-obstacle environments. Our aim is to solve an open problem in navigation within such environments: the feasible space partitioning in accordance with the distribution of obstacles. It is shown that such a partitioning is a key concept towards the generation of a corridor in cluttered environments. Once a corridor between an initial and a final position is generated, the selection of a path is considerably simplified in comparison with the methods which explore the original non-convex feasible regions of the environment. The core of the methodology presented here is the construction of a convex lifting which boils down to a convex optimization. The paper covers both the mathematical foundations and the computational details of the implementation and aims to illustrate the concepts with geometrical examples.

Review of path planning of welding robot based on spline curve

“…Various path planning algorithms arise one after another over a long period of investigation by different scholars. Ioan et al [55], proposed a feasible spatial partitioning method to solve the path generation problem in multi-obstacle environments. Riazi et al [56], using intelligent algorithms to reduce energy consumption and peak power of industrial robots.…”

Real-Time Quadrotor Trajectory Optimization with Time-Triggered Corridor Constraints

“…For Assumption 1 to hold, we need to know a priori the ordered sequence of corridors that order in which the optimal trajectory traverses. Many corridor generating algorithms, such as convex lifting, can provide such an ordered sequence of corridors; see [3,4] for some recent examples.…”

“…Along such a trajectory, the position of the quadrotor needs to stay within a set of collision-free corridors. Each corridor is a bounded convex flight space; the union of all these corridors form a nonconvex pathway connecting the quadrotor's current position to its target position [3,4]; see Since the flight space defined by the union of the corridors is nonconvex, optimizing the trajectories for the quadrotor is computationally challenging. One standard solution approach is mixed integer programming [5][6][7], which first uses binary variables to describe the union of all corridors, then optimizes quadrotor trajectories together with these binary variables [8][9][10][11].…”

Computational load reduction of the agent guidance problem using Mixed Integer Programming

“…Alternatively, [38] obtains large ellipsoidal regions of convex obstacle-free space in intricate environments with a greedy convex segmentation technique and [31] provides an entirely collision-free path with reduced number of integer variables. In turn, [39] divides large and complex environments into smaller segments through many pre-processing steps, [40] uses convex optimization to obtain target defect areas and [41] builds a convex lifting which partitions the space and descends to convex optimization.…”