This paper presents a methodology for treating energy consistency when considering multiple simultaneous impacts and contacts with friction in the simulation of systems of multiple interconnected bodies. Hard impact and contact is considered where deformation of the impacting surfaces is negligible. The proposed approach uses a discrete algebraic model of impact in conjunction with moment and tangential co-efficients of restitution (CORs) to develop a general impact law for determining post-impact velocities. This process depends on impulse-momentum theory, complementarity conditions, a principle of maximum dissipation, and the determination of contact forces. The proposed methodology also uses an energy-modifying COR to directly control the system's energy. The approach is illustrated on a bicycle-like structure.

This paper presents a novel gait generation technique for legged robotic systems which utilizes the dynamic capability equations. The method consists of calculating the acceleration capability early in the simulation to determine a specific configuration which easily allows a gait to be generated. This position is calculated to most effectively arrest any body center-of-mass momentum upon impact and allows the system to continue travelling in the desired direction without suffering detrimental effects from the impulse forces normally encountered when walking.

Kinematically redundant manipulators have been proven to offer certain advantages over more heavily constrained systems. One such advantage is the extra degrees-of-freedom can be used for other tasks such as maintaining a posture which affords higher acceleration capability in the direction of the desired motion. However certain issues arise when considering the control of these mechanisms due to the lack of invertability of the rectangular Jacobian matrix. Here this issue is addressed by augmenting the rectangular Jacobian with a characterization of the null space motions. This approach allows for a gradient-based control scheme, based upon the dynamic capability equations, to increase or maintain the local performance capability of a manipulator as it performs some task. Simulation results of the application of this control scheme to a six degree-of-freedom (DOF) planar manipulator are given to illustrate the control's advantages on a highly redundant system.