Nima Shafii

A hybrid method of fuzzy simulation and genetic algorithm to optimize constrained inventory control systems with stochastic replenishments and fuzzy demand

Multi-periodic inventory control problems are mainly studied by employing one of two assumptions. First, the continuous review, where depending on the inventory level, orders can happen at any time, and next the periodic review, where orders can only be placed at the beginning of each period. In this paper, we relax these assumptions and assume the times between two replenishments are independent random variables. For the problem at hand, the decision variables (the maximum inventory of several products) are of integer-type and there is a single space-constraint. While demands are treated as fuzzy numbers, a combination of back-order and lost-sales is considered for the shortages. We demonstrate the model of this problem is of an integer-nonlinear-programming type. A hybrid method of fuzzy simulation (FS) and genetic algorithm (GA) is proposed to solve this problem. The performance of the proposed method is then compared with the performance of an existing hybrid FS and simulated annealing (SA) algorithm through three numerical examples containing different numbers of products. Furthermore, the applicability of the proposed methodology along with a sensitivity analysis on its parameters is shown by numerical examples. The comparison results show that, at least for the numerical examples under consideration, the hybrid method of FS and GA shows better performance than the hybrid method of FS and SA.

Evolution of biped walking using truncated fourier series and particle swarm optimization

Controlling a biped robot with a high degree of freedom to achieve stable and straight movement patterns is a complex problem. With growing computational power of computer hardware, high resolution real time simulation of such robot models has become more and more applicable. This paper presents a novel approach to generate bipedal gait for humanoid locomotion. This approach is based on modified Truncated Fourier Series (TFS) for generating angular trajectories. It is also the first time that Particle Swarm Optimization (PSO) is used to find the best angular trajectory and optimize TFS. This method has been implemented on Simulated NAO robot in Robocup 3D soccer simulation environment (rcssserver3d). To overcome inherent noise of the simulator we applied a Resampling algorithm which could lead the robustness in nondeterministic environments. Experimental results show that PSO optimizes TFS faster and better than GA to generate straighter and faster humanoid locomotion.

Biped walking using coronal and sagittal movements based on truncated fourier series

Biped walking by using all joint movements and DOFs in both directions (sagittal plane and coronal plane) is one of the most complicated research topics in robotics. In this paper, angular trajectories of a stable biped walking for a humanoid robot are generated by a Truncated Fourier Series (TFS) approach. The movements of legs and arms in sagittal plane are implemented by an optimized gait generator and a new model is proposed that can also produce the movement of legs in coronal plane based on TFS. Particle Swarm Optimization (PSO) is used to find the best angular trajectories and optimize TFS. Experimental results show that the using joints movements in sagittal and coronal planes to compose the walking skill allowed the biped robot to walk faster than previous methods that only used the joints in sagittal plane.

Humanoid behaviors: from simulation to a real robot

This paper presents the modifications needed to adapt a humanoid agent architecture and behaviors from simulation to a real robot. The experiments were conducted using the Aldebaran Nao robot model. The agent architecture was adapted from the RoboCup 3D Simulation League to the Standard Platform League with as few changes as possible. The reasons for the modifications include small differences in the dimensions and dynamics of the simulated and the real robot and the fact that the simulator does not create an exact copy of a real environment. In addition, the real robot API is different from the simulated robot API and there are a few more restrictions on the allowed joint configurations. The general approach for using behaviors developed for simulation in the real robot was to: first, (if necessary) make the simulated behavior compliant with the real robot restrictions, second, apply the simulated behavior to the real robot reducing its velocity, and finally, increase the velocity, while adapting the behavior parameters, until the behavior gets unstable or inefficient. This paper also presents an algorithm to calculate the three angles of the hip that produce the desired vertical hip rotation, since the Nao robot does not have a vertical hip joint. All simulation behaviors described in this paper were successfully adapted to the real robot.

Learning to Walk Fast: Optimized Hip Height Movement for Simulated and Real Humanoid Robots

The linear inverted pendulum model has been used predominantly to generate balanced humanoid walking. This model assumes that the hip height is fixed during the walk. In this paper, generating a fast walk is studied with the main focus on the effect of hip height movement. Our approach is based on modeling the hip height movement and learning its parameters in order to generate a fast walk. The hip height trajectory is generated using Fourier basis functions. The generated trajectory is the input to programmable Central Pattern Generators (CPGs) in order to modulate generated trajectories smoothly. The inverted pendulum model is utilized to model a balanced walking. A numerical approach is presented to control inverted pendulum dynamics. Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is employed to search for appropriate hip height trajectory and walking parameters that optimize walking speed. This approach has been tested not only to obtain fast forward walk but also a fast side walk. Experiments are conducted on both simulated and real NAO robots. The results show that the change from the learned forward walk to learned side walk is performed stably, which confirm the important role of using CPGs. The comparison of the results of the proposed gait model (and development approach) with those obtained using fixed hip height also shows that fixed height walking is slower than variable height walking.

Omnidirectional Walking and Active Balance for Soccer Humanoid Robot

Soccer Humanoid robots must be able to fulfill their tasks in a highly dynamic soccer field, which requires highly responsive and dynamic locomotion. It is very difficult to keep humanoids balance during walking. The position of the Zero Moment Point (ZMP) is widely used for dynamic stability measurement in biped locomotion. In this paper, we present an omnidirectional walk engine, which mainly consist of a Foot planner, a ZMP and Center of Mass (CoM) generator and an Active balance loop. The Foot planner, based on desire walk speed vector, generates future feet step positions that are then inputs to the ZMP generator. The cart-table model and preview controller are used to generate the CoM reference trajectory from the predefined ZMP trajectory. An active balance method is presented which keeps the robot’s trunk upright when faced with environmental disturbances. We have tested the biped locomotion control approach on a simulated NAO robot. Our results are encouraging given that the robot has been able to walk fast and stably in any direction with performances that compare well to the best RoboCup 2012 3D Simulation teams.

A Truncated Fourier Series with genetic algorithm for the control of biped locomotion

Humanoid research has made notable progress during the past 25 years. However, currently most humanoids use the ZMP (Zero Moment Point) for control of bipedal locomotion, which requires precise modeling and actuation with high control gains. On the contrary, researchers do not rely on such precise modeling and actuation. In this paper we have tried to introduce a novel method for the evolution of walking behavior in a simulated humanoid robot with up to 22 degrees of freedom. In this method a modified Truncated Fourier Series (TFS) generates walking angular trajectories and it is optimized by genetic algorithm. By studying human walking TFS parameters have also been reduced. As a test-bed, we chose Robocup 3D soccer simulation environment (spark) and implemented our method in MRL 3D teams agents. Experimental results show that training of the robot can be successfully performed by our method, thus allowing the biped robot to walk fast, stably and straightly.

Omnidirectional Walking with a Compliant Inverted Pendulum Model

In this paper, we propose a novel omnidirectional walking engine that achieves energy efficient, human like, stable and fast walking. We augment the 3D inverted pendulum with a spring model to implement a height change in the robot’s center of mass trajectory. This model is used as simplified model of the robot and the zero moment point (ZMP) criterion is used as the stability indicator. The presented walking engine consists of 5 main modules including the “next posture generator” module, the “foot trajectory generator” module, the “center of mass (CoM) trajectory generator” module, the “robot posture controller” module and “Inverse kinematics (IK) solver” module. The focus of the paper is the generation of the position of the next step and the CoM trajectory generation. For the trajectory generator, we extend the 3D-IPM with an undamped spring to implement height changes of the CoM. With this model we can implement active compliance for the robot’s gait, resulting in a more energy efficient movement. We present a modified method for solving ZMP equations which derivation is based on the new proposed model for omnidirectional walking. The walk engine is tested on simulated and a real NAO robot. We use policy search to optimize the parameters of the walking engines for the standard 3D-LIPM and our proposed model to compare the performance of both models each with their optimal parameters. We optimize the policy parameters in terms of energy efficiency for a fixed walking speed. The experimental results show the advantages of our proposed model over 3D-LIPM.

Development of an Omnidirectional Walk Engine for Soccer Humanoid Robots

Humanoid soccer robots must be able to carry out their tasks in a highly dynamic environment which requires responsive omnidirectional walking. This paper explains a new omnidirectional walking engine for a humanoid soccer robot that mainly consists of a foot planner, a zero moment point (ZMP) trajectory generator, a centre of mass (CoM) calculator and an active balance feedback loop. An analytical approach is presented for generating the CoM trajectory, in which the cart-table motion of the equations is solved using the Fourier approximation of the ZMP. With this approach, we propose using a new time segmentation approach in order to parametrize the double-support phase. An active balance method is also proposed which keeps the robots trunk upright when faced with environmental disturbances.The walking engine is tested on both simulated and real NAO robots. Our results are encouraging given the fact that the robot performs favourably, walking quickly and in a stable manner in any direction in comparison...

Learning a fast walk based on ZMP control and hip height movement

The Linear inverted pendulum model is widely used in biped walking approaches. This model assumes that the hip height is fixed while the robot walks. In this paper, the hip height movement, or vertical Center of Mass (CoM) trajectory, is used by a robot to achieve a faster and more stable walk. For the first time, the hip height movement is modeled in a formal way and its parameters are learned. The inverted pendulum model and a numerical approach are used to control the Zero Moment Point (ZMP) for generating a balanced walk. Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is applied to optimize the hip height trajectory and walking parameters with respect to walking speed and stability. Experimental results are achieved on a simulated NAO robot. A comparison of the results of the proposed gait model (and development approach) with those obtained using fixed hip height shows that fixed height walking is slower than variable height walking.