Bipedal robot walks stably on slopes using optimized joint movements
Walking on the Slope: Stable Bipedal Gaits with Genetic-Algorithm-Optimized Trajectories
Robotics
Summary
Walking robots need to move their legs carefully to stay balanced, especially on hills. The paper shows how a robot with 8 moving parts can walk steadily on flat ground and slopes up to 22.5 degrees by planning its leg movements using math and computer algorithms. The robot’s movements are fine-tuned with a genetic algorithm that chooses the easiest walking style to lower energy use while keeping balance. Stability depends more on how the robot’s weight is spread out than its total weight. If the robot tries to walk too fast or on steeper slopes, it might tip over unless its steps or feet are changed.
What this means in practice
- •For robotics engineers: Design stable and energy-efficient walking patterns for biped robots operating on slopes up to 22.5 degrees.
- •For prosthetics developers: Enhance prosthetic leg control algorithms by incorporating optimized trajectories that consider terrain inclination and balance.
Authors
Madhav Rijal
Abstract
This paper presents the kinematic and dynamic modeling, trajectory generation, and stability analysis of an 8-degree-of-freedom (DOF) biped robot walking on flat and inclined terrain. Denavit-Hartenberg (DH) parameters and homogeneous transformations are used to derive the forward kinematics, while closed-form inverse kinematics maps the desired hip and swing-foot Cartesian trajectories, generated with cubic splines, to joint angles. Joint torques are computed using the Newton-Euler iterative algorithm, and dynamic stability is evaluated using the zero moment point (ZMP) criterion. A genetic algorithm (GA) optimizes the hip height, maximum swing-foot lift, and frontal-plane tilt angle by minimizing the work done by the joints subject to a ZMP feasibility penalty. Simulation results in MATLAB show that the nominal 8-DOF model remains ZMP-stable for step completion times down to 0.5 s and for slope inclinations up to 22.5 degrees with the given foot geometry. Beyond these limits, the ZMP leaves the support polygon, and either the foot dimensions or the trajectory parameters must be modified. The results also show that ZMP stability is governed by the mass distribution among the links rather than the total mass of the robot.