Multiphase Trajectory Generation for Planar Biped Robot Using Direct Collocation Method

Stability and energy efficiency are the main focuses in the bipedal robot field. In this paper, we apply a multiphase gait, which is different from the widely used two-phase gait, to improve the stability at the moment, when a biped robot transfers from the double support phase to the single support phase. Then, we create dynamic equations with contact forces in each phase using Lagrangian formulation. Furthermore, the direct collocation method is utilized to generate the optimal trajectory toward both stability and energy efficiency. Finally, the comparison between multiphase gait and two-phase gait is performed with numerical simulations. The results prove that multiphase gait increases the stability margin in the cost of slightly decreasing energy efficiency. Besides, both gaits show a similar human-like characteristic in hip height variation during walking.

Trajectory Optimization Using Analytical Target Cascading

In the previous reports, analytical target cascading (ATC) is generally applied to product optimization. In this paper, the application area of ATC is expanded to trajectory optimization. Direct collocation method is utilized to convert a trajectory optimization into a nonlinear programing (NLP) problem. The converted NLP is a large-scale problem with sparse matrix of functional dependence table (FDT) suitable for the application of ATC. Three numerical case studies are provided to show the effects of ATC in solving trajectory optimization problems.

A Decentralized Approach for Multi-Subsystem Co-Design Optimization Using Direct Collocation Method

Multi-subsystem co-design refers to the simultaneous optimization of physical plant and controller of a system decomposed into multiple interconnected co-design subsystems. In this paper, a new decentralized approach based on the direct collocation and decomposition-based optimization methods is formulated to solve multi-subsystem co-design problems. First, the problem is decomposed into physical plant and control parts. In the control part, the entire time horizon is discretized into subintervals and grid points. In this way, a continuous optimal control problem is converted into a finite dimensional nonlinear programming (NLP) problem. The optimality condition decomposition (OCD) method is employed to decompose and solve the converted NLP problem in a decentralized manner. Next, the dual decomposition method is used to optimize the plant part. Finally, the plant and control parts are connected by the gradients of Hamiltonian with respect to the plant variables. The proposed approach is applied to two examples. First, a numerical example is presented to illustrate the approach step-by-step. Then in the second example, a spring-mass-damper system is solved. For both examples, the solutions obtained by the proposed decentralized approach are compared against a centralized (all-in-one) approach.

Trajectory Optimization for a Cruising Unmanned Aerial Vehicle Attacking a Target at Back Slope While Subjected to a Wind Gradient

The trajectory of a tubular launched cruising unmanned aerial vehicle is optimized using the modified direct collocation method for attacking a target at back slope under a wind gradient. A mathematical model of the cruising unmanned aerial vehicle is established based on its operational and motion features under a wind gradient to optimize the trajectory. The motion characteristics of “altitude adjustment” and “suicide attack” are taken into full account under the combat circumstance of back slope time key targets. By introducing a discrete time function, the trajectory optimization is converted into a nonlinear programming problem and the SNPOT software is applied to solve for the optimal trajectory of the missile under different wind loads. The simulation results show that, for optimized trajectories, the average attack time decreased by up to 29.1% and the energy consumption is reduced by up to 25.9% under specified wind gradient conditions.A,ωdire, andWmaxhave an influence on the flight trajectories of cruising unmanned aerial vehicle. This verifies that the application of modified direct collocation method is reasonable and feasible in an effort to achieve more efficient missile trajectories.

Dynamic Optimization of Ship Boiler Startup Based on Modelica and JModelica.org

Apply optimization method to reduce the startup time can improve the maneuverability of vessel and reduce the operation cost of the unit. In this paper, a boiler system model was developed to capture system dynamic and the variety of stress based on the multi-domain modeling language Modelica, then the optimization model was built taking minimize the start-up time as optimization targets, constrained on the thermal and mechanical stress. The optimization process was performed on the platform of JModelica.org, exploiting the direct collocation method. Fuel quantity curve of the start up phase was optimized. Using the optimized fuel quantity curve, the boiler startup time could be reduced without reducing the drum boiler life.