Optimal Motion Generation for Groups of Robots: A Geometric Approach

2004 ◽  
Vol 126 (1) ◽  
pp. 63-70 ◽  
Author(s):  
Calin Belta ◽  
Vijay Kumar
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Mobile Robots ◽  
Configuration Space ◽  
Geodesic Flow ◽  
Geometric Approach ◽  
General Treatment ◽  
Rectilinear Motion ◽  
Motion Generation ◽  
Optimal Motion

In this paper we generate optimal smooth trajectories for a set of fully-actuated mobile robots. Given two end configurations, by tuning one parameter, the user can choose an interpolating trajectory from a continuum of curves varying from that corresponding to maintaining a rigid formation to motion of the robots toward each other. The idea behind our method is to change the original constant kinetic energy metric in the configuration space and can be summarized into three steps. First, the energy of the motion as a rigid structure is decoupled from the energy of motion along directions that violate the rigid constraints. Second, the metric is “shaped” by assigning different weights to each term. Third, geodesic flow is constructed for the modified metric. The optimal motions generated on the manifolds of rigid body displacements in 3-D space SE3 or in plane SE2 and the uniform rectilinear motion of each robot corresponding to a totally uncorrelated approach are particular cases of our general treatment.

scholarly journals Safe Path Planning Algorithms for Mobile Robots Based on Probabilistic Foam

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4156
Author(s):  
Luís B. P. Nascimento ◽  
Dennis Barrios-Aranibar ◽  
Vitor G. Santos ◽  
Diego S. Pereira ◽  
William C. Ribeiro ◽  
...  
Keyword(s):  
Path Planning ◽  
Mobile Robots ◽  
Configuration Space ◽  
Autonomous Robot ◽  
Breadth First Search ◽  
Propagation Process ◽  
Robot Systems ◽  
And Performance ◽  
Safe Path ◽  
High Clearance

The planning of safe paths is an important issue for autonomous robot systems. The Probabilistic Foam method (PFM) is a planner that guarantees safe paths bounded by a sequence of structures called bubbles that provides safe regions. This method performs the planning by covering the free configuration space with bubbles, an approach analogous to a breadth-first search. To improve the propagation process and keep the safety, we present three algorithms based on Probabilistic Foam: Goal-biased Probabilistic Foam (GBPF), Radius-biased Probabilistic Foam (RBPF), and Heuristic-guided Probabilistic Foam (HPF); the last two are proposed in this work. The variant GBPF is fast, HPF finds short paths, and RBPF finds high-clearance paths. Some simulations were performed using four different maps to analyze the behavior and performance of the methods. Besides, the safety was analyzed considering the new propagation strategies.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals The Rotating Rigid Body Model Based on a Non-twisting Frame

2020 ◽  
Vol 30 (6) ◽  
pp. 3199-3233 ◽  
Author(s):  
Cristian Guillermo Gebhardt ◽  
Ignacio Romero
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Conservation Laws ◽  
Rotation Rate ◽  
Governing Equations ◽  
New Model ◽  
Body Model ◽  
Integration Schemes ◽  
Rigid Body Model ◽  
Unit Vectors

Abstract This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations.

scholarly journals Non-Smooth Geodesic Flows and Classical Mechanics

1969 ◽  
Vol 12 (2) ◽  
pp. 209-212 ◽  
Author(s):  
J. E. Marsden
Keyword(s):  
Phase Space ◽  
Kinetic Energy ◽  
Hamiltonian Systems ◽  
Configuration Space ◽  
Smooth Function ◽  
Cotangent Bundle ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Geodesic Flows ◽  
Image Position

As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by

scholarly journals Energy Modeling and Experimental Validation of Four-Wheel Mecanum Mobile Robots for Energy-Optimal Motion Control

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1372
Author(s):  
Liang Zhang ◽  
Jongwon Kim ◽  
Jie Sun
Keyword(s):  
Power Consumption ◽  
Mobile Robots ◽  
Motion Control ◽  
Prediction Accuracy ◽  
Experimental Validation ◽  
Control Method ◽  
Energy Modeling ◽  
Optimal Motion ◽  
Consumption Model ◽  
Mecanum Wheel

Four-wheel Mecanum mobile robots (FWMRs) are widely used in transportation because of their omnidirectional mobility. However, the FWMR trades off energy efficiency for flexibility. To efficiently predict the energy consumption of the robot movement processes, this paper proposes a power consumption model for the omnidirectional movement of an FWMR. A power consumption model is of great significance for reducing the power consumption, motion control, and path planning of robots. However, FWMRs are highly maneuverable, meaning their control is complicated and their energy modeling is extremely complex. The speed, distance, path, and power consumption of the robot can vary greatly depending on the control method. This energy model was mathematically implemented in MATLAB and validated by our laboratory’s Mecanum wheel robot. The prediction accuracy of the model was over 95% through simulation and experimental verification.

EB-RRT: Optimal Motion Planning for Mobile Robots

2020 ◽  
Vol 17 (4) ◽  
pp. 2063-2073 ◽  
Author(s):  
Jiankun Wang ◽  
Max Q.-H. Meng ◽  
Oussama Khatib
Keyword(s):  
Motion Planning ◽  
Mobile Robots ◽  
Optimal Motion ◽  
Optimal Motion Planning
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