Optimal Trajectory Generation Method Research Articles

Optimal trajectory generation method to find a smooth robot joint trajectory based on multiquadric radial basis functions

Optimal trajectory generation method to find a smooth robot joint trajectory based on multiquadric radial basis functions

Trajectory planning and control for drone replacement for multidrone cinematography

This work addresses the problem of trajectory planning and control for a team of drones, so that a vehicle that is following a target as part of a multi-vehicle formation flight can be safely replaced with minimum impact on the formation objectives. An optimal trajectory generation method is presented, which relies on formulating a nonlinear optimization problem with constraints imposed by the physical limitations of the vehicle, the formation, and the surrounding environment, including nonlinear constraints to enforce inter-vehicle collision avoidance and clear visibility of the target. An online planning and control strategy is also implemented through a Nonlinear Model Predictive Control problem, based on the dynamic model of the system, a quadratic objective function, and a set of constraints, that again include collision avoidance and clear visibility. The proposed algorithms are validated in software-in-the-loop simulations that include the autopilot software.

Vertical Trajectory Optimization to Minimize Environmental Impact in the Presence of Wind

The vertical trajectory optimization for the en route descent phase is studied in the presence of both along-track and cross winds, which are both modeled as functions of altitude. The flight range covers some portion of a cruise segment and ends at a meter fix. The descent trajectory is assumed as a flight idle descent. The problem is formulated as an optimal control problem with both mixed state path constraints and pure state constraints. For minimizing environmental impacts, we optimize descent trajectory with respect to two cost functionals: fuel and emissions costs. We analyze both singular arc and boundary arc using the necessary conditions of the optimality. From the analysis result, we propose the optimal trajectory generation method, in which the optimal trajectory is generated by the backward and forward integration. The trajectory from the proposed algorithm is compared with the numerical optimal solution of the original optimal control problem. The result shows that the proposed algorithm generates the same solution as the numerical optimal solution. The wind speed, windshear, and cross-wind effects on the optimal trajectory are analyzed with two aircraft type, Boeing 737-500 and Boeing 767-400.

Gait optimization of biped robots based on human motion analysis

This paper proposes a dynamically stable and optimal trajectory generation method for biped robots to walk up and down stairs, based on human motion analysis, since a human walks efficiently without high energy consumption, and the energy-efficient locomotion pattern results in a more natural walking pattern. Seven important elements of the human gait on stairs are identified in the analysis of the motion data captured from subjects. Those factors enable us to generate trajectories of biped robots similar to that of human beings walking up-and-down stairs. The dynamics of the robot and human are different in weight distribution, degree of freedom and so on. A real-coded genetic algorithm as an optimization tool is used to produce the optimized gait for the robot and to improve the energy autonomy and stability. Various computer simulations were performed based on a 12-DOF biped robot model with which many of the essential characteristics of the human walking motion on stairs can be captured. The proposed method exhibits its efficiency in quickly finding an optimal trajectory, which is due to not only the nature of genetic algorithms but also a small number of design variables employed. Thus, this makes it possible to generate various locomotion trajectories of biped robots simply by appropriately changing some of the boundary conditions.

Optimal trajectory generation for biped robots walking up-and-down stairs

This paper proposes an optimal trajectory generation method for biped robots for walking up-and-down stairs using a Real-Coded Genetic Algorithm (RCGA). The RCGA is most effective in minimizing the total consumption energy of a multi-dof biped robot. Each joint angle trajectory is defined as a 4-th order polynomial of which the coefficients are chromosomes or design variables to approximate the walking gait. Constraints are divided into equalities and inequalities. First, equality constraints consist of initial conditions and repeatability conditions with respect to each joint angle and angular velocity at the start and end of a stride period. Next, inequality constraints include collision prevention conditions of a swing leg, singular prevention conditions, and stability conditions. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot model that consists of seven links in the sagittal plane. The optimal trajectory is more efficient than that generated by the Modified Gravity-Compensated Inverted Pendulum Mode (MGCIPM). And various trajectories generated by the proposed GA method are analyzed from the viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.