This paper presents a trajectory planner for humanoid robots based on nonlinear model predictive control that can generate trajectories with variable center of mass heights and adaptive foot positions in real-time. This is done by analytically formulating the zero moment point constraint as a quadratic function that includes the vertical center of mass state. This constraint is then combined with linear foot position constraints, constraints on the vertical center of mass state and a quadratic goal function to form a quadratically constrained quadratic program. This program is then solved via sequential quadratic programing. It can be solved in less than 5 ms on average with a 3.4 Ghz CPU by taking advantage of the fact that the analytic problem formulation allows the analytical gradients to be computed, thus time consuming numerical differentiation is avoided and the gradient computation time is reduced from 12.4 ms to 0.12 ms. An experiment on a 3.5 Kg robot is conducted to verify the effectiveness of this algorithm in walking on a terrain where the two feet are at different heights. Lastly it is shown via simulation that the proposed approach can improve disturbance recovery capacity by up to 7%.

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A bipedal robot should be robust and able to move in various directions on stairs. However, up to date many research studies have been focusing on walking in the up or down direction only. Therefore, a strategy to realize walking along a step is investigated. In conventional methods, CoM is moved up or down during walking in this situation. In this paper, a method named as Dual Length Linear Inverted Pendulum Method (DLLIPM) with Newton-Raphson is proposed for 3-D biped robot walking. The proposed method applies different length of pendulum at left and right legs in order to represent the CoM height. By using the proposed method, maximum impact forces are reduced. From the Ground Reaction Forces (GRF) data obtained in the simulations, the validity of the proposed method is confirmed.

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This paper proposes a method to automatically limit referential joint torques of a biped robot to prevent the feet from losing contact with the ground. This method can be used to implement active balancing, which is equivelent to position control as long as the torque limits are not exceeded. Therefore, unlike the zero-moment point feedback methods, the proposed method is robust against disturbances and has a good trajectory following ability without having the usual dangers associated with stiff, position-controlled methods. Furthermore, this method is based on force sensor data, and thus unlike inverse dynamic methods, it is robust to variations in robot dynamics that can arise when the robot carries loads. This paper also proposes a method to limit referential joint velocities to prevent overshoot of the robot. This is useful when the robots center of mass (COM) position moves near the edge of the support polygon, because if the COM exits the support polygon due to overshoot, then it will not be able to return to it. These two proposals are then combined to form a position control system that is robust against overshoot and can strongly interact with the environment without losing contact of the feet with the ground. Finally, this position control system is implemented on the biped robot MARI-3, and it is shown that near-zero overshoot position control with compliance is achieved.