In this study, a gait optimization routine is developed to generate walking patterns which demand the lowest friction forces for implementation. The aim of this research is to fully address the question "which walking pattern demands the lowest coefficient of friction amongst all feasible patterns?". To this end, first, the kinematic structure of the considered 31 DOF (Degrees of Freedom) humanoid robot is investigated and a closed-form dynamics model for its lower-body is developed. Then, the medium through which the walking pattern generation is conducted is presented. In this medium, after designing trajectories for the feet and the pelvis, the joint space variables are obtained, using the inverse kinematics. Finally, by employing a genetic algorithm (GA), an optimization process is conducted to generate walking patterns with the minimum Required Coefficient Of Friction (RCOF). Six parameters are adopted to parameterize the pelvis trajectory and are exploited as the design variables in this optimization procedure. Also, a parametrical study is accomplished to address the effects of some other variables on RCOF. For comparison purposes, a tip-over Stability Margin (SM) is defined, and an optimization procedure is conducted to maximize this margin. Finally, the proposed gait planning procedure is implemented on SURENA III, a humanoid robot designed and fabricated in CAST, to validate the developed simulation procedure. The obtained results reveal merits of the proposed optimal gait planning procedure in terms of RCOF.

SUMMARYAdding active toe joints to a humanoid robot structure has lots of difficulties such as mounting a small motor and an encoder on the robot feet. Conversely, adding passive toe joints is simple, since it only consists of a spring and a damper. Due to lots of benefits of implementing passive toe joints, mentioned in the literature, the goal of this study is to add passive toe joints to the SURENA III humanoid robot which was designed and fabricated at the Center of Advanced Systems and Technologies (CAST), University of Tehran. To this end, a simple passive toe joint is designed and fabricated, at first. Then, stiffness and damping coefficients are calculated using a vision-based measurement. Afterwards, a gait planning routine for humanoid robots equipped with passive toe joints is implemented. The tip-over stability of the gait is studied, considering the vibration of the passive toe joints in swing phases. The multi-body dynamics of the robot equipped with passive toe joints are presented using the Lagrange approach. Furthermore, system identification routine is adopted to model the dynamic behaviors of the power transmission system. By adding the calculated actuating torques for these two models, the whole dynamic model of the robot is computed. Finally, the performance of the proposed approach is evaluated by several simulations and experimental results. Results show that using passive toe joints reduces energy consumption of ankle and knee joints by 15.3% and 9.0%, respectively. Moreover, with relatively large values of stiffness coefficients, the required torque and power of the knee and hip joints during heel-off motion reduces as the ankle joint torque and power increases.

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In this paper, an online adaptation algorithm for bipedal walking on uneven surfaces with height uncertainty is proposed. In order to generate walking patterns on flat terrains, the trajectories in the task space are planned to satisfy the dynamic balance and slippage avoidance constraints, and also to guarantee smooth landing of the swing foot. To ensure smooth landing of the swing foot on surfaces with height uncertainty, the preplanned trajectories in the task space should be adapted.The proposed adaptation algorithm consists of two stages. In the first stage, once the swing foot reaches its maximum height, the supervisory control is initiated until the touch is detected. After the detection, the trajectories in the task space are modified to guarantee smooth landing. In the second stage, this modification is preserved during the Double Support Phase (DSP), and released in the next Single Support Phase (SSP). Effectiveness of the proposed online adaptation algorithm is experimentally verified through realization of the walking patterns on the SURENA III humanoid robot, designed and fabricated at CAST. The walking is tested on a surface with various flat obstacles, where the swing foot is prone to either land on the ground soon or late.

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