Multitasking collision-free optimal motion planning algorithms in Euclidean spaces

We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions. Our algorithms are optimal in a very concrete sense, namely, they have the minimal possible number of local planners. Our algorithms are motivated by those presented by Mas-Ku and Torres-giese (as streamlined by Farber), and are developed within the more general context of the multitasking (a.k.a. higher) motion planning problem. In addition, an eventual implementation of our algorithms is expected to work more efficiently than previous ones when applied to systems with a large number of moving objects.

PGD Variational vademecum for robot motion planning. A dynamic obstacle case

A fundamental robotics task is to plan collision-free motions for complex bodies from a start to a goal position among a set of static and dynamic obstacles. This problem is well known in the literature as motion planning (or the piano mover's problem). The complexity of the problem has motivated many works in the field of robot path planning. One of the most popular algorithms is the Artificial Potential Field technique (APF). This method defines an artificial potential field in the configuration space (C-space) that produces a robot path from a start to a goal position. This technique is very fast for RT applications. However, the robot could be trapped in a deadlock (local minima of the potential function). The solution of this problem lies in the use of harmonic functions in the generation of the potential field, which satisfy the Laplace equation. Unfortunately, this technique requires a numerical simulation in a discrete mesh, making useless for RT applications. In our previous work, it was presented for the first time, the Proper Generalized Decomposition method to solve the motion planning problem. In that work, the PGD was designed just for static obstacles and computed as a vademecum for all Start and Goal combinations. This work demonstrates that the PGD could be a solution for the motion planning problem. However, in a realistic scenario, it is necessary to take into account more parameters like for instance, dynamic obstacles. The goal of the present paper is to introduce a diffusion term into the Laplace equation in order to take into account dynamic obstacles as an extra parameter. Both cases, isotropic and non-isotropic cases are into account in order to generalize the solution.

Efficient motion generation for a six-legged robot walking on irregular terrain via integrated foothold selection and optimization-based whole-body planning

SUMMARYIn this paper, an efficient motion planning method is proposed for a six-legged robot walking on irregular terrain. The method provides the robot with fast-generated free-gait motions to traverse the terrain with medium irregularities. We first of all introduce our six-legged robot with legs in parallel mechanism. After that, we decompose the motion planning problem into two main steps: first is the foothold selection based on a local footstep cost map, in which both terrain features and the robot mobility are considered; second is a whole-body configuration planner which casts the problem into a general convex optimization problem. Such decomposition reduces the complexity of the motion planning problem. Along with the two-step planner, discussions are also given in terms of the robot-environmental relationship, convexity of constraints and robot rotation integration. Both simulations and experiments are carried out on typical irregular terrains. The results demonstrate effectiveness of the planning method.

Lagrangian Jacobian Motion Planning: A Parametric Approach

This paper addresses the motion planning problem of nonholonomic robotic systems. The system’s kinematics are described by a driftless control system with output. It is assumed that the control functions are represented in a parametric form, as truncated orthogonal series. A new motion planning algorithm is proposed based on the solution of a Lagrange-type optimisation problem stated in the linear approximation of the parametrised system. Performance of the algorithm is illustrated by numeric computations for a motion planning problem of the rolling ball.