Linear State Feedback Controller Design for Bipedal Locomotion Safwan Choudhury Department of Electrical and Computer Engineering University of Waterloo schoudhury@uwaterloo.ca Abstract—Bipedal locomotion is a highly active area of re- search within the field of humanoid robotics. Thus far, the most popular control strategy used to achieve walking in robots has been based on the Zero-Moment Point (ZMP) criterion. In order to achieve stable gait cycles for a humanoid robot, the walking control strategy must track a stable COM trajectory which keeps the ZMP location within the region of foot support. A simplified motion model for the walking robot is obtained by approximating the complex dynamics of the system as a 3D linear inverted pendulum (3D LIPM). This approximation provides a casual, linear time-invariant (LTI) system which can be controlled using linear techniques. It was determined that the state space model of the 3D LIPM is both controllable and observable. However, the system is inherently unstable due to poles in the right half plane. In order to stabilize the system, a linear state feedback system is designed. The final control strategy is implemented in simulation on a 14DOF lower body humanoid research platform which closely models the kinematic and dynamic parameters of a physical robot. It was determined that the linear control strategy utilizing state feedback was successful in keeping the ZMP within the region of foot support. Index Terms—Bipedal Locomotion, Humanoid Robotics, Zero- Moment Point, Passive Dynamics, Gait Analysis, Linear Inverted Pendulum, State Feedback I. I NTRODUCTION As the general field of robotics continues to advance and gain widespread popularity, one class of robots have a unique advantage of being able to navigate through human-designed environments with minimal changes to the surrounding infrastructure [1]. Humanoid robotics and bipedal robots in general, mimic the natural human form of transportation by moving robotic links to achieve two-legged locomotion. The ultimate end goal of this area of research is fairly straight forward: achieve dynamically stable walking which closely resembles human gait. A. Existing Research There have been several different emerging fronts in the field of bipedal locomotion. These include biologically inspired techniques which use neural networks [2], central pattern generators [3] and other oscillator-based approaches [4] to control and generate walking motion. Other approaches aim to use control theory to drive the system dynamics in some predefined way (i.e. angular momentum control [5] or hybrid zero dynamics [6]). However, there are two leading Fig. 1. Lower body humanoid research platform to investigate bipedal locomotion research with 14 DOF (3 DOF hip, 1 DOF knee and 3 DOF ankle). techniques which dominate most of bipedal locomotion research today: 1) Zero-Moment Point: The most popular technique to achieve dynamically stable walking has been through control strategies based on the ZMP criterion [7]. Since its inception nearly 40 years ago, ZMP has been used as a measure of balance. The underlying concept states that there exists a point on the ground where the dynamic reaction forces acting on the system cancel out and do not produce a moment in the horizontal direction (i.e. the zero-moment point). If this point