Foot Trajectory Planning Method with Adjustable Parameters for Complex Environment In order to ensure a stable and continuous walking of the quadruped robot in complex environment, a low impact foot trajectory planning method for walk gait is proposed. Firstly, a fourlegged robot singleleg model with three active degrees of freedom and one passive degree of freedom is constructed. The kinematics analysis is carried out, and the foot trajectory tracking controller based on motion space is designed. Then the singleleg motion of the robot in complex environment is analysed, and the foot trajectory based on the 3rdorder bezier curve satisfying the obstacle condition is proposed. After that the method of parameter determination is further clarified. In order to reduce the impact force between the foot and the ground, the sigmoid function is introduced to process the foot trajectory. The simulation results show that through the improved bezier method, the impact between the foot and the ground can be effectively reduced.

Online Relative Footstep Optimization for Legged Robots Dynamic Walking Using DiscreteTime Model Predictive Control We present a unified control framework that generates dynamic walking motions for biped and quadruped robots with online relative footstep optimization. The footstep optimization is formulated as a discretetime Model Predictive Control problem which determines future footstep locations. The framework has a hierarchical structure consisting of three layers: footstep planner, trajectory generator and wholebody controller. The footstep planner plans next footstep position based on Linear Inverted Pendulum (LIP) model. Relative footstep optimization is proposed to enable automatic footstep planning without the use of any predefined footstep sequences. The trajectory generator will generate CoM and feet trajectory given the next footstep placement. In order to generalize to quadruped robots, xe2x80x9cvirtual legxe2x80x9d concept has been used to coordinate leg pair movement. The wholebody inverse dynamic controller calculates joint torques to track given Cartesian reference trajectories. To include underactuation into consideration, contact vertices formulation of ground reaction forces (GRFs) has been adopted. Generalized wholebody controller can handle biped robot with line feet as well as quadruped robots with point feet walking with dynamic gaits. Several simulations have been performed to demonstrate the robustness and generality of the proposed framework.