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The influence of ankle compliance on bipedal robot locomotion is investigated in this paper. The focus is on reduction of energy consumption. The concept of hybrid zero dynamics is adapted to design walking gaits with three phases: underactuated heel roll, full actuation and underactuated toe roll. Ankle springs work in parallel with the ankle actuators. Stiffness and offset of the linear torsional springs at the ankle and gait parameters are optimized simultaneously. It is shown that simultaneous optimization of spring properties and gait is superior to optimizing the spring after the gait. Optimal spring stiffness and offset lead to a major reduction in energy consumption. Furthermore, a more human-like gait is observed for simultaneous optimization of gait and spring parameters compared to gait optimization with zero stiffness.

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The potential areas of application for robots have gradually extended beyond the classical industrial settings in largescale enterprizes: nowadays, the integration of robots into daily life has become a central development in robotics. Here, one major challenge is the physical interaction with unknown and/or changing environments. Such an interaction requires knowledge of the exchanged contact forces and torques. To this end, robotic systems are typically equipped with force/torque sensors at the wrist. By using force control schemes that rely on measurements from these sensors, conventional manipulation tasks are successfully executed. In particular, for dynamic manipulation tasks, however, the problem arises that the inertial forces/torques of the end effector have a non-negligible effect on the measurements of the wrist sensor. This degrades the performance of the interaction control and constitutes a safety risk since the actual interaction forces/torques deviate from the desired values. As a solution to this problem, the paper discusses four contact force/torque observer designs: two approaches are based on the extended Kalman filter (EKF) and two approaches are based on the unscented Kalman filter (UKF). For both types, EKF and UKF, two different measurement vectors are considered: the first one only uses pose and force/torque measurements, whereas the second one also uses acceleration measurements to determine the contact forces and torques. The four observer designs are evaluated in simulation and experiment for six-degree-of-freedom (DOF) tasks.

The concept of virtual holonomic constraints is extended to the case of double support, which is characterized by a closed kinematic chain and redundancy in the state variables. An appropriate coordinate transformation is used to present the equations of motion in the coordinates of the actual degrees of freedom of the system. Virtual constraints of proper dimension lead to reduced dynamics of dimension two. The reduced dynamics is derived in a generalized way which includes previous results for the case of a single point contact. Control of the reduced dynamics is discussed in particular for the double support case. The derived concept is illustrated for a biped robot walking gait with a double support phase and an underactuated single support phase.