• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.2
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• pp.111-119
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• 1996

In this paper, we propose time-optimal trajectory planning algorithms for cooperative multi-robot manipulators system considering optimal load distribution. Internal forces essentially effect on time optimal trajectory planning and if they are comitted, the time optimal scheme is not no longer true. Therefore, we try to find the internal force factors of cooperative robot manipulators system in a time-optimal aspect. In this approach, a specific generalized inverse is used and is fuzzified for the purpose. In this optimal method, the fuzzy logic concept is used and selected for diminishing computation time, for finding the load distribution factors.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.1
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• pp.42-54
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• 2009

Contrast to the 6-DOF nonlinear dynamic modeling of nonlinear tracking problem, 3-DOF point-mass modeling of flight mechanics is efficient and adequate for applying the trajectory optimization problem. There exist limitations to apply an optimal trajectory from point-mass modeling as a reference trajectory directly to conduct the nonlinear tracking control, In this paper, new matching trajectory optimization scheme is proposed to compensate those differences of mismatching. To verify performance of proposed method, full ascent three-dimensional flight trajectories are obtained by reflecting the real constraints of flight conditions and airship performance with and without jet stream condition. Then, they are compared with the optimal trajectories obtained from conventional method.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.5
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• pp.471-476
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• 2015

This paper presents a maximum velocity trajectory planning algorithm for differential mobile robots with wheel velocity constraint to cope with physical limits in the joint space for two-wheeled mobile robots (TMR). In previous research, the convolution operator was able to generate a central velocity that deals with the physical constraints of a mobile robot while considering the heading angles along a smooth curve in terms of time-dependent parameter. However, the velocity could not track the predefined path. An algorithm is proposed to compensate an error that occurs between the actual and driven distance by the velocity of the center of a TMR within a sampling time. The velocity commands in Cartesian space are also converted to actuator commands to drive two wheels. In the case that the actuator commands exceed the maximum velocity the trajectory is redeveloped with the compensated center velocity. The new center velocity is obtained according to the curvature of the path to provide a maximum allowable velocity meaning a time-optimal trajectory. The effectiveness of the algorithm is shown through numerical examples.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.4 s.181
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• pp.75-82
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• 2006

In this paper, we propose an optimal trajectory for biped robots to move up-and-down stairs using a genetic algorithm and a computed-torque control for biped robots to be dynamically stable. First, a Real-Coded Genetic Algorithm (RCGA) which of operators are composed of reproduction, crossover and mutation is used to minimize the total energy. Constraints are divided into equalities and inequalities: Equality constraints consist of a position condition at the start and end of a step period and repeatability conditions related to each joint angle and angular velocity. Inequality constraints include collision avoidance conditions of a swing leg at the face and edge of a stair, knee joint conditions with respect to the avoidance of the kinematic singularity, and the zero moment point condition with respect to the stability into the going direction. In order to approximate a gait, each joint angle trajectory is defined as a 4-th order polynomial of which coefficients are chromosomes. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot that consists of seven links in the sagittal plane. The trajectory is more efficient than that generated by the modified GCIPM. And various trajectories generated by the proposed GA method are analyzed in a viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.7 s.172
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• pp.112-121
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• 2005

This paper is concerned with smooth trajectory generation of biped robot which has inverted pendulum type balancing weight. Genetic algorithm is used to generate the trajectory of the leg and balancing weight. Balancing trajectory can be determined by solving the second order differential equation under the condition that the reference ZMP (Zero moment point) is settled. Reference ZMP effect on gait pattern absolutely but the problem is how to determine the reference ZMP. Genetic algorithm can find optimal solution under the high order nonlinear situation. Optimal trajectory is generated when use genetic algorithm which has some genes and a fitness function. In this paper, minimization of balancing joints motion is used for the fitness function and set the weight factor of the two balancing joints at the fitness function. Inverted pendulum type balancing weight is very similar with human and this model can be used fur humanoid robot. Simulation results show ZMP trajectory and the walking experiment made on the real biped robot IWR-IV.

• The Journal of Korea Robotics Society
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• v.8 no.2
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• pp.92-103
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• 2013

Humanoid robot is the most intimate robot platform suitable for human interaction and services. Biped walking is its basic locomotion method, which is performed with combination of joint actuator's rotations in the lower extremity. The present work employs humanoid robot simulator and numerical optimization method to generate optimal joint trajectories for biped walking. The simulator is developed with Matlab based on the robot structure constructed with the Denavit-Hartenberg (DH) convention. Particle swarm optimization method minimizes the cost function for biped walking associated with performance index such as altitude trajectory of clearance foot and stability index concerning zero moment point (ZMP) trajectory. In this paper, instead of checking whether ZMP's position is inside the stable region or not, reference ZMP trajectory is approximately configured with feature points by which piece-wise linear trajectory can be drawn, and difference of reference ZMP and actual one at each sampling time is added to the cost function. The optimized joint trajectories realize three phases of stable gait including initial, periodic, and final steps. For validation of the proposed approach, a small-sized humanoid robot named DARwIn-OP is commanded to walk with the optimized joint trajectories, and the walking result is successful.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.742-748
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• 2004

In this paper are presented TSTO system analysis including some controlled variables on the engine operation such as a fuel flow rate and a pressure ratio of compressor, as well as variables on the trajectory. TSTO studied here is accelerated up to Mach 6 by a fly-back booster powered by air breathing engines. Three different types of engine cycle were treated for propulsion system of the booster, such as a turbo ramjet, a precooled turbojet and an EXpander cycle Air Turbo Ramjet (ATREX). The history of the controlled variables on the engine operation was optimized by Sequential Quadratic Programming (SQP) to accomplish the minimum fuel consumption. The trajectory was also optimized simultaneously. The results showed that the turbo ramjet gave the best fuel consumption. The optimal trajectory was almost the same except in the transonic range and just before reaching to Mach 6. The history of the pressure ratio of compressor considerably depended on the engine type. It is concluded that simultaneous optimization for engine control and trajectory is effective especially for a high-speed airplane propelled by turbojets like the TSTO booster.

• Advances in aircraft and spacecraft science
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• v.6 no.5
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• pp.391-407
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• 2019

Flight trajectory optimization has become an important factor not only to reduce the operational costs (e.g.,, fuel and time related costs) of the airliners but also to reduce the environmental impact (e.g.,, emissions, contrails and noise etc.) caused by the airliners. So far, these factors have been dealt with in the context of 2D and 3D trajectory optimization, which are no longer efficient. Presently, the 4D trajectory optimization is required in order to cope with the current air traffic management (ATM). This study deals with a cubic spline approximation method for solving 4D trajectory optimization problem (TOP). The state vector, its time derivative and control vector are parameterized using cubic spline interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into nonlinear programming problem (NLP). The proposed method is successfully applied to the generation of a minimum length optimal trajectories along 4D waypoints, where the method generated smooth 4D optimal trajectories with very accurate results.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1402-1407
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• 2004

Moving a fragile object from an initial point to a goal location in minimum time without damage is pursued in this paper. In order to achieve the goal, first of all, the range of maximum acceleration and velocity are specified, which the manipulator can generate dynamically on the path that is planned a priori considering the geometrical constraints. Later, considering the impulsive force constraint of the object, the range of maximum acceleration and velocity are going to be obtained to keep the object safe while the manipulator is carrying it along the curved path. Finally, a time-optimal trajectory is planned within the maximum allowable range of the acceleration and velocity. This time optimal trajectory planning can be applied for real applications and is suitable for not only a continuous path but also a discrete path.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1136-1139
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• 1996

For on-line trajectory planning such as teleoperation it is desirable to keep good manipulability of the robot manipulators since the motion command is not given in advance. To keep good manipulability means the capability of moving any arbitrary directions of task space. An optimization process with different manipulability measures are performed and compared for a redundant robot system moving in 2-dimensional task space, and gives results that the conventional manipulability ellipsoid based on the Jacobian matrix is not good choice as far as the optimal direction of motion is concerned.