Contingency Model Predictive Control for Bipedal Locomotion on Moving Surfaces with a Linear Inverted Pendulum Model

Gait control of legged robotic walkers on dynamically moving surfaces (e.g., ships and vehicles) is challenging due to the limited balance control actuation and unknown surface motion. We present a contingent model predictive control (CMPC) for bipedal walker locomotion on moving surfaces with a linear inverted pendulum (LIP) model. The CMPC is a robust design that is built on regular model predictive control (MPC) to incorporate the "worst case" predictive motion of the moving surface. Integrated with an LIP model and walking stability constraints, the CMPC framework generates a set of consistent control inputs considering to anticipated uncertainties of the surface motions. Simulation results and comparison with the regular MPC for bipedal walking are conducted and presented. The results confirm the feasibility and superior performance of the proposed CMPC design over the regular MPC under various motion profiles of moving surfaces.

Foot Shape-Dependent Resistive Force Model for Bipedal Walkers on Granular Terrains

Legged robots have demonstrated high efficiency and effectiveness in unstructured and dynamic environments. However, it is still challenging for legged robots to achieve rapid and efficient locomotion on deformable, yielding substrates, such as granular terrains. We present an enhanced resistive force model for bipedal walkers on soft granular terrains by introducing effective intrusion depth correction. The enhanced force model captures fundamental kinetic results considering the robot foot shape, walking gait speed variation, and energy expense. The model is validated by extensive foot intrusion experiments with a bipedal robot. The results confirm the model accuracy on the given type of granular terrains. The model can be further integrated with the motion control of bipedal robotic walkers.

Biomechanical Comparison of Human Walking Locomotion on Solid Ground and Sand

Current studies on human locomotion focus mainly on solid ground walking conditions. In this paper, we present a biomechanic comparison of human walking locomotion on solid ground and sand. A novel dataset containing 3-dimensional motion and biomechanical data from 20 able-bodied adults for locomotion on solid ground and sand is collected. We present the data collection methods and report the sensor data along with the kinematic and kinetic profiles of joint biomechanics. A comprehensive analysis of human gait and joint stiffness profiles is presented. The kinematic and kinetic analysis reveals that human walking locomotion on sand shows different ground reaction forces and joint torque profiles, compared with those patterns from walking on solid ground. These gait differences reflect that humans adopt motion control strategies for yielding terrain conditions such as sand. The dataset also provides a source of locomotion data for researchers to study human activity recognition and assistive devices for walking on different terrains.

A Reduced-Order Resistive Force Model for Robotic Foot-Mud Interactions

Legged robots are well-suited for broad exploration tasks in complex environments with yielding terrain. Understanding robotic foot-terrain interactions is critical for safe locomotion and walking efficiency for legged robots. This paper presents a reduced-order resistive-force model for robotic-foot/mud interactions. We focus on vertical robot locomotion on mud and propose a visco-elasto-plastic analog to model the foot/mud interaction forces. Dynamic behaviors such as mud visco-elasticity, withdrawing cohesive suction, and yielding are explicitly discussed with the proposed model. Besides comparing with dry/wet granular materials, mud intrusion experiments are conducted to validate the force model. The dependency of the model parameter on water content and foot velocity is also studied to reveal in-depth model properties under various conditions. The proposed force model potentially provides an enabling tool for legged robot locomotion and control on muddy terrain.

Energy Efficient Foot-Shape Design for Bipedal Walkers on Granular Terrain

It is important to understand how bipedal walkers balance and walk effectively on granular materials, such as sand and loose dirt, etc. This paper first presents a computational approach to obtain the motion and energy analysis of bipedal walkers on granular terrains and then discusses an optimization method for the robot foot-shape contour design for energy efficiently walking. We first present the foot-terrain interaction characteristics of the intrusion process using the resistive force theory that provides comprehensive force laws. Using human gait profiles, we compute and compare the ground reaction forces and the external work for walking gaits with various foot shapes on granular terrains. A multi-objective optimization problem is finally formulated for the foot contour design considering energy saving and walking efficiency. It is interesting to find out a non-convex foot shape gives the best performance in term of energy and locomotion efficiency on hard granular terrains. The presented work provides an enabling tool to further understand and design efficient and effective bipedal walkers on granular terrains.