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Dynamic gait planning for humanoid robots encounters difficulties such as stability, speed, and smoothness. In most of previous studies, joints' trajectories are calculated in 3D Cartesian space, then, introducing boundary conditions and using polynomials, the first and second derivatives of the motion are ensured to be continuous. Then, the stability of the motion is guaranteed using Zero Moment Point (ZMP) stability criterion. In this study, a trajectory planner is presented using the semi-ellipse equations of the motion; the continuity of the derivatives is preserved. Stabilization of motion is attained through using ZMP criterion and 3d inverted pendulum equations in three slope... 

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect... 

A new methodology has been proposed which offers a systematic approach to use the so called "performance index" or cost function as the basic tool to incorporate the dynamics of the aircraft in the process of trajectory planning. Moreover, by using non-dimensional parameters a better understanding of the dynamic terms are provided. © 2005 IEEE  

This paper presents a new approach for trajectory planning of manipulator robots based on Virtual Potential Field (VPF) in presence of static obstacles. In this method, a series of via points between starting point and goal point is obtained by traverse end-effector of manipulator in affected by different VPF while avoiding obstacles in the Cartesian space. An optimum trajectory is generated by using pattern search algorithm which determines strength of potential fields to minimize the value of desired objective function. Cubic splines are used to generate a smooth trajectory through path points in joint space that are obtained by inverse kinematics solution of corresponding points in the... 

A new methodology has been proposed to enhance inverse dynamics applications in the process of trajectory planning and optimization in terrain following flights (TFFs). The new approach uses a least square scheme to solve a general two-dimensional (2-D) TFF in a vertical plane. In the mathematical process, Chebyshev polynomials are used to model the geographical data of the terrain in a given route in a manner suitable for the aircraft at hand. The aircraft then follows the modeled terrain with sufficient clearance. In this approach the terrain following (TF) problem is effectively converted to an optimal tracking problem. Results show that this method provides a flexible approach to solve... 

A central problem in motor control is to understand how the many biomechanical degrees of freedom are coordinated to achieve a goal. A common assumption is that Central Nervous System (CNS) would minimize a performance index to achieve this goal which is called objective function. In this paper, two popular objective functions are utilized to design the optimal trajectory of trunk movements. A 3D computational method incorporated with 18 anatomically oriented muscles is used to simulate human trunk system. Inverse dynamics allows us to compute torque which is generated around Lumbosacral joint. This torque is divided among muscles by static stability-based optimization. Trunk movement from... 

A novel approach in minimum time trajectory planning in Terrain Following/Terrain Avoidance (TF/TA) flight is proposed. In this research, terrain is understood based on fuzzy logic and small changes in terrain are omitted. Another novelty is constructing a relationship between slope of terrain and aircraft height with speed of aircraft by fuzzy approach. Finally after a decision making process and based on governing dynamics and cost function, trajectory is constructed by a polynomial. This method is state of the art in literature  

A novel approach in Terrain Following/Terrain Avoidance (TF/TA) flight is proposed that facilitates flying over unknown terrains. Intelligency is implemented using fuzzy decision making tools. This method can be used in offline design in trajectory planning which has wide applications in TF/TA. A relationship b etween slope of terrain and aircraft height with speed of aircraft is constructed by fuzzy approach  

In this paper, the problem of Optimal Trajectory Planning for a high speed planing boat under nonlinear equality and inequality path constraints, is addressed. First, a nonlinear mathematical model of the craft's dynamic is constructed. To solve a trajectory optimization problem, we can utilize the indirect or direct methods. In the indirect methods, the maximum principle of Pontryagin is used to transform the optimal control problem into Euler-Lagrange equations, on the other hand, in the direct methods it is necessary to transcribe the optimal control problem into a nonlinear programming problem (NLP) by discretization of states and controls. The resulted NLP can be solved by... 

Computational models of the central nervous system after a stroke helps to reveal the physiological mechanisms that may have strong impacts on the neuro-motor rehabilitation approaches. This paper studies the stroke subject's motor control mechanism in reaching movements by extending the previous study by incorporating the kinematics of motion as well as neural disconnection between the muscles and the CNS to further develop a planar patient specific neuro-musculoskeletal model of arm. The developed model was calibrated to eight post-stroke individuals by altering the Muscle Significance Factors (MFS) using numerical optimization to match the simulated motions with those measured... 

This paper deals with control of the brachiation robot. The brachiation is a type of mobile robot that moves from branch to branch like a long-armed ape. Here, as a new innovation, Pontryagin's minimum principle is used to obtain the optimal trajectories for two different problems. The first problem is "Brachiation between fixed branches with different distance and height" and the second is "Brachiating and catching the moving target branch". Theoretical results show that the control effort in the proposed method is reduced by 25% in comparison with the "Target Dynamics" method which was proposed in prior articles for this robot. The obtained optimal trajectory also minimizes the brachiation... 

Purpose - The purpose of this paper is to devise a new approach to synthesize closed-loop feedback guidance law for online thrust- insensitive optimal trajectory generation utilizing neural networks. Design/methodology/approach - The proposed methodology utilizes an open- loop variational formulation that initially determines optimal launch/ ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open-loop optimized trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually produce thrust-insensitive closed-loop optimal guidance laws...