Model Predictive Control for Motion Planning of Quadrupedal Locomotion

Abstract

This paper is motivated to transfer the model predictive control approach used in bipedal locomotion to formulate gait planning of quadrupedal robots. The particular lateral-sequence gait of quadrupeds is treated as an equivalence to the bipedal walking. The Model Predictive Control (MPC) algorithm uses 3D-Linear Inverted Pendulum Model for representing the center of mass dynamics for planning the quadrupedal gaits, and a dimensionless discretetime state-space formulated is derived for MPC. Subsequently, the footholds can be generated automatically via optimization of quadratic programming (QP) without the need of a separate footstep planner. The generated walking gaits were implemented and validated first in the physics simulation of a quadruped named EHbot, and then the effectiveness of the proposed method was further demonstrated through our experiments. Both simulation and experimental data are presented and analyzed for evaluating the performance.

Heavy-duty hexapod robot sideline tipping judgment and recovery

“…According to Table II, leg 6 should be selected as the adjustment leg. Based on equation (15), the adjustment time is 0.74 s, with the target foothold point at (−2390, −1908, −1741). After leg 6 lands as a stance leg, the robot stability margin rises from below 20 to around 40, significantly improving stability.…”

“…Currently, legs 1 and 3 have the maximum force at the foot, and leg 2 should be selected as the adjustment. Based on equation (15), the adjustment time is 2.1 s, with the target foothold point at (0, 1894, −1783). After leg 2 lands as a stance leg, the stability margin of the robot increases from below 20 to about 21.5.…”

“…Otherwise, it is deemed unstable. The Zero Moment Point (ZMP) is a typical dynamic stability margin criteria for legged robots, and it has been modified and applied numerous times to robot stability control, gait planning, foot force distribution, and other robot motion control [15, 16]. Another notable criterion in this category is the FASM [17].…”

Mechanical design and force control algorithm for a robot leg with hydraulic series-elastic actuators

“…Based on the motion planning of quadrupedal locomotion, the trajectories of each foot are generated by walking pattern generation in task space, namely Cartesian space. 30 Therefore, we use an impedance model in Cartesian space to deal with foot-ground interactions. 24,25 The desired forces f d in Cartesian space generated by the Cartesian space impedance model can be calculated by…”