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A variety of regulations are involved in the design of an automobile frontal structure. The regulations are pedestrian protection, the Federal Motor Vehicle Safety Standard (FMVSS) part 581 bumper test, and the Research Council for Automobile Repairs (RCAR) test. The frontal structure consists of the bumper system and a crash box that connects the bumper system and the main body. The detailed design of the bumper system is performed to meet two conditions: first, regulation for pedestrian protection (lower-legform impact test); second, FMVSS part 581. In the two regulations, the stiffness requirements of the bumper system conflict with each other. In order to meet lower leg protection, a relatively soft bumper system is required, while a relatively stiff system is typically needed to manage the pendulum impact. A new bumper system is proposed by adding new components and is analysed by using the non-linear finite element method. An optimization problem is formulated to incorporate the analysis results. Each regulation is considered as a constraint from a loading condition, and two loading conditions are used. Response surface approximation optimization is utilized to solve the formulated problem. RCAR requires reduction in the repair cost when an accident happens. The repair cost in a low-speed crash could be reduced by using an energy-absorbing structure such as the crash box. The crash box is analysed by using the non-linear finite element method. An optimization problem for the crash box is formulated to incorporate the analysis results. Discrete design using orthogonal arrays is utilized to solve the formulated problem in a discrete space.

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An online asymmetric trajectory generation method for biped robots is proposed to maintain dynamical postural stability and increase energy autonomy, based on the running stability criterion defined in phases. In a support phase, an asymmetric trajectories for the hip and swing leg of the biped robots is obtained from an approximated running model with two springless legs and a spring-loaded inverted pendulum model so that the zero moment point should exist inside the safety boundary of a supporting foot, and the supporting leg should absorb large reaction forces, take off and fly through the air. The biped robot is underactuated with six degrees of under-actuation during flight. The trajectory generation strategies for the hip and both legs in a flight phase use the approximated running model and non-holonomic constraints based on the linear and angular momenta at the mass center. Next, we present an impedance control with a force modulation strategy to guarantee a stable landing on the ground and simultaneously track the desired trajectories where the desired impedance at the hip link and both legs is specified. A series of computer simulations for two different types of biped robots show that the proposed running trajectory and impedance control method Electronic supplementary material The online version of this article (http://dx.satisfy the two conditions for running stability and make the biped robot more robust to variations in the desired running speed, gait transitions between walking and running, and parametric modeling errors. We have examined the feasibility of this method with running experiments on a 12-DOF biped robot without arms. The biped robot could run successfully with average forward speed of about 0.3359 [m/s].