Quasi Optimal Gait of a Biped Robot with a Rolling Knee Kinematic

In this paper, we address the problem of optimization of trajectories for a new class of biped robot. The knees of this biped are similar as the anthropomorphic one and have a rolling contact between the femur and the tibia. The robot has seven mechanical links and six actuators. The walking gait considered is a succession of single support phase (SSP) and impact of the mobile foot with the ground. Cubic uniform spline functions defined on a time interval express the gait for one step. An energy consumption function and a torques quadratic function are used to compare the new robot with anthropomorphic knees to a conventional robot with revolute joint knees. The minimization of the criteria is made with simplex algorithm. The physical constraints concerning the ZMP and the mobile foot behavior are respectively checked to make a step. Simulation results show that the energy consumption of the new biped with rolling knee contact is less than that of the robot with revolute joint knees.ANR R2A

Optimal Walking of an Underactuated Planar Biped with Segmented Torso

Recently, underactuated bipeds with pointed feet have been studied to achieve dynamic and energy efficient robot walking patterns. However, these studies usually simplify a robot torso as one link, which is different from a human torsos containing 33 vertebrae. In this paper, therefore, we study the optimal walking of a 6-link planar biped with a segmented torso derived from its 5-link counterpart while ensuring that two models are equivalent when the additional torso joint is locked. For the walking, we suppose that each step is composed of a single support phase and an instantaneous double support phase, and two phases are connected by a plastic impact mapping. In addition, the controlled outputs named symmetry outputs capable of generating exponentially stable orbits using hybrid zero dynamics, are adopted to improve physical interpretation. The desired outputs are parameterized by B´ezier functions, with 5-link robot having 16 parameters to optimize and 6-link robot having 19 parameters. According to our energy criterion, the segmented torso structure may reduce energy consumption up to 8% in bipedal walking, and the maximum energy saving is achieved at high walking speeds, while leaving the criteria at low walking speeds remain similar for both robots.China CSC LCF

Adaptive Excitation Control for the Underactuated Biped Robot

AbstractA control method to make the chaotic gait converge to a stable cycle gait is proposed for the biped robot with knees. This control method is called adaptive excitation control. It is based on the principle of bionics and the principle of self-excited. The control law is a combination of sinusoidal input and sensory feedback control. The control torque is only inputted into the robot's hip. Therefore, the walking process is low energy consuming. Simulation results show that the control method proposed in this paper is effective. It can enlarge the basin of attraction of limit cycle and increase the gait stability

Stability analysis and control for bipedal locomotion using energy methods

In this thesis, we investigate the stability of limit cycles of passive dynamic walking. The formation process of the limit cycles is approached from the view of energy interaction. We introduce for the first time the notion of the energy portrait analysis originated from the phase portrait. The energy plane is spanned by the total energy of the system and its derivative, and different energy trajectories represent the energy portrait in the plane. One of the advantages of this method is that the stability of the limit cycles can be easily shown in a 2D plane regardless of the dimension of the system. The energy portrait of passive dynamic walking reveals that the limit cycles are formed by the interaction between energy loss and energy gain during each cycle, and they are equal at equilibria in the energy plane. In addition, the energy portrait is exploited to examine the existence of semi-passive limit cycles generated using the energy supply only at the take-off phase. It is shown that the energy interaction at the ground contact compensates for the energy supply, which makes the total energy invariant yielding limit cycles. This result means that new limit cycles can be generated according to the energy supply without changing the ground slope, and level ground walking, whose energy gain at the contact phase is always zero, can be achieved without actuation during the swing phase. We design multiple switching controllers by virtue of this property to increase the basin of attraction. Multiple limit cycles are linearized using the Poincare map method, and the feedback gains are computed taking into account the robustness and actuator saturation. Once a trajectory diverges from a basin of attraction, we switch the current controller to one that includes the trajectory in its basin of attraction. Numerical simulations confirm that a set of limit cycles can be used to increase the basin of attraction further by switching the controllers one after another. To enhance our knowledge of the limit cycles, we performed sophisticated simulations and found all stable and unstable limit cycles from the various ground slopes not only for the symmetric legs but also for the unequal legs that cause gait asymmetries. As a result, we present a novel classification of the passive limit cycles showing six distinct groups that are consecutive and cyclical