Sampling-Based Methods for Motion Planning with Constraints

Abstract

Robots with many degrees of freedom (e.g., humanoid robots and mobile manipulators) have increasingly been employed to accomplish realistic tasks in domains such as disaster relief, spacecraft logistics, and home caretaking. Finding feasible motions for these robots autonomously is essential for their operation. Sampling-based motion planning algorithms are effective for these high-dimensional systems; however, incorporating task constraints (e.g., keeping a cup level or writing on a board) into the planning process introduces significant challenges. This survey describes the families of methods for sampling-based planning with constraints and places them on a spectrum delineated by their complexity. Constrained sampling-based methods are based on two core primitive operations: (a) sampling constraintsatisfying configurations and (b) generating constraint-satisfying continuous motion. Although this article presents the basics of sampling-based planning for contextual background, it focuses on the representation of constraints and sampling-based planners that incorporate constraints. 3.1

Optimal Robot Motion Planning of Redundant Robots in Machining and Additive Manufacturing Applications

“…In this way, the modulus of Cartesian velocity is constant when t ∈ [4,16], as shown in Figure 8. The considered robot model is a 6-DoF Comau NS16, while the algorithm runs on a laptop equipped with a Intel Core i7-8565U, 16 GB RAM-LPDDR3 and a 512 GB SSD.…”

“…For example, one might want to keep the robot tool oriented toward the floor during the whole trajectory for safety reasons. Recent works addresssed problem of this kind when the closed form of the constraints is not known a priori [16,17]. In this paper, we consider a more specific but still important class of trajectories, in which the number of degrees of freedom of the task is smaller than the one of the robot.…”

“…It is worth stressing that, in this kind of tasks, path constraints are known a priori. This is a fundamental difference with respect to [16], because the dimension of the problem can be reduced by only exploring the subspace given by the kinematic redundancy.…”

Multiquery Motion Planning in Uncertain Spaces: Incremental Adaptive Randomized Roadmaps

“…Such an ability is provided using a motion planning procedure. Motion planning can be defined as moving a mobile robot between a pair of start and goal configurations in an environment filled with obstacles, while avoiding any collision with obstacles and the environments boundaries (Kingston et al, 2018;Klaučo et al, 2016). It has been proven that the motion planning problem in its simplest form is NP-complete (Canny, 1988;González et al, 2016), meaning that the running time of the algorithm is exponential in the degree of freedom which makes the motion planning problem a challenging research area.…”

Learning the Metric of Task Constraint Manifolds for Constrained Motion Planning

“…To solve the above-mentioned problems, various methods of motion planning on constraint manifold are widely proposed, including relaxation [9,10], projection [11][12][13], tangent-space [14] and atlas [15,16]. The characteristics of these methods are summarized and compared in [17]. Relaxation is to relax the surface of the constraint manifold by increasing the allowed tolerance of the constraint function so that the sampling-based planners can handle the constraints without additional machinery.…”