Closed‐form solution for real‐time optimal walking pattern generation constrained by the desired amount of capture point

2021 ◽  
Author(s):  
Sangsin Park
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Pattern Generation ◽  
Walking Pattern ◽  
Time Optimal ◽  
Walking Pattern Generation ◽  
Capture Point

A performance comparison between closed form and numerical optimization solutions for humanoid robot walking pattern generation

2021 ◽  
Vol 18 (4) ◽  
pp. 172988142110297
Author(s):  
Samer A Mohamed ◽  
Shady A Maged ◽  
Mohammed I Awad
Keyword(s):  
Power Consumption ◽  
Closed Form ◽  
Numerical Optimization ◽  
Humanoid Robot ◽  
Closed Form Solution ◽  
Computational Effort ◽  
Form Solution ◽  
Pattern Generation ◽  
Walking Pattern ◽  
Walking Pattern Generation

This article presents the modeling process of the lower part of a humanoid biped robot in terms of kinematic/dynamic states and the creation of a full dynamic simulation environment for a walking robot using MATLAB/Simulink. This article presents two different approaches for offline walking pattern generation: one relying on a closed-form solution of the linear inverted pendulum model (LIPM) mathematical model and another that considers numerical optimization as means of desired output trajectory following for a cart table state-space model. This article then investigates the possibility of introducing solution-dependent modifications to both approaches that could increase the reliability of basic walking pattern generation models in terms of smooth single support–double support phase transitioning and power consumption optimization. The algorithms were coded into offline walking pattern generators for NAO humanoid robot as a valid example and the two approaches were compared against each other in terms of stability, power consumption, and computational effort as well as against their basic unmodified counterparts.

Real Time Trajectory Modification Using a Closed Form Solution

1992 ◽  
Author(s):  
Michael R. Hummels ◽  
Raymond J. Cipra
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Interval ◽  
Efficient Manner ◽  
Planning Strategy ◽  
Higher Derivatives ◽  
On Line ◽  
Line Trajectory

Abstract An on-line trajectory modification and path planning strategy is developed which will allow a robot to respond in an efficient manner to real time sensory input. The approach developed here eliminates the need for solving many equations by developing a closed form algorithm. It uses two fourth order curves for the transition phases with a constant velocity section in between. Although this is done by providing additional constraints to the curve, it makes the problem of determining the trajectory much easier to solve, while providing continuous higher derivatives. It also provides a safe and efficient way of modifying trajectories based on the robots joint rate limits, joint acceleration limits, jerk limits, and desired time interval between trajectory modifications for a 4-1-4 trajectory. This method involves the solution of one second order equation and is directed toward real time applications.

scholarly journals Closed-form solution of discrete-time optimal control and its convergence

2018 ◽  
Vol 12 (3) ◽  
pp. 413-418 ◽  
Author(s):  
Hehong Zhang ◽  
Yunde Xie ◽  
Gaoxi Xiao ◽  
Chao Zhai
Keyword(s):  
Optimal Control ◽  
Closed Form ◽  
Discrete Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Optimal Control ◽  
Time Optimal

scholarly journals PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 195
Author(s):  
Andrea D’Ambrosio ◽  
Andrea Carbone ◽  
Dario Spiller ◽  
Fabio Curti
Keyword(s):  
Real Time ◽  
Inverse Dynamics ◽  
A Priori ◽  
Closed Form Solution ◽  
Control Policy ◽  
Form Solution ◽  
Soft Landing ◽  
Lunar Landing ◽  
Optimal Guidance ◽  
Time Optimal

The problem of real-time optimal guidance is extremely important for successful autonomous missions. In this paper, the last phases of autonomous lunar landing trajectories are addressed. The proposed guidance is based on the Particle Swarm Optimization, and the differential flatness approach, which is a subclass of the inverse dynamics technique. The trajectory is approximated by polynomials and the control policy is obtained in an analytical closed form solution, where boundary and dynamical constraints are a priori satisfied. Although this procedure leads to sub-optimal solutions, it results in beng fast and thus potentially suitable to be used for real-time purposes. Moreover, the presence of craters on the lunar terrain is considered; therefore, hazard detection and avoidance are also carried out. The proposed guidance is tested by Monte Carlo simulations to evaluate its performances and a robust procedure, made up of safe additional maneuvers, is introduced to counteract optimization failures and achieve soft landing. Finally, the whole procedure is tested through an experimental facility, consisting of a robotic manipulator, equipped with a camera, and a simulated lunar terrain. The results show the efficiency and reliability of the proposed guidance and its possible use for real-time sub-optimal trajectory generation within laboratory applications.

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