Biped Robot Balance Control via Sinusoidal Limit Cycle
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Solution Overview
Problem
Biped walking robots using finite state machine (FSM) control methods face instability in balancing on a two-dimensional space due to limit cycles that tend to converge or diverge, leading to non-smooth shapes and instability.
Innovation Solution
Setting control angles for the robot's ankles using a sinusoidal function to maintain a stable closed loop within a limit cycle, considering the center of gravity and states of the FSM, ensuring the limit cycle forms a stable closed loop by controlling angles and angular velocities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If a limit cycle is applied to control the biped robot's balance using FSM states, then the robot can balance on a two-dimensional space, but the limit cycle tends to converge or diverge causing instability and non-smooth shapes
Solution Approach 1:
The patent applies periodic sinusoidal functions to generate control angles for the biped robot's ankles. The control angle is defined as a sinusoidal function of time, creating a periodic control action that ensures the limit cycle forms a smooth closed loop. This periodic approach prevents convergence or divergence issues by maintaining consistent oscillatory motion patterns that naturally form stable closed loops in the phase plane.
2Stability of the object's composition
If control angles are set to balance the robot, then the robot can maintain equilibrium, but the control angles may cause the limit cycle to form non-smooth shapes when converging or diverging
Solution Approach 1:
The patent changes the parameter representation of control angles from linear or polynomial functions to sinusoidal functions. This parameter change ensures that the control angle and its derivative (control angular velocity) form a smooth closed loop in the phase plane. The sinusoidal parameterization guarantees smooth transitions and eliminates sharp corners or discontinuities in the limit cycle shape, as sine functions are inherently smooth and periodic.
3Stability of the object's composition
If the limit cycle forms a stable closed loop, then the robot achieves smooth balance control, but requires precise control of both control angles and control angular velocities
Solution Approach 1:
The patent implements a feedback mechanism where the control system continuously monitors the robot's actual state (angles and angular velocities) and compares it with the desired sinusoidal control trajectories. The feedback ensures that the system remains on the stable limit cycle by making real-time adjustments. This feedback loop maintains the stable closed loop formation while managing the complexity through a structured control architecture that processes angle and angular velocity information systematically.
Data Source
AI summary
An finite state machine (FSM)-based biped walking robot, to which a limit cycle is applied to balance the robot right and left on a two-dimensional space, and a method of controlling balance of the robot. In order to balance an FSM-based biped walking robot right and left on a two-dimensional space, control angles to balance the robot according to states of the FSM-based biped walking robot are set, and the control angles are controlled using a sinusoidal function to allow relations between the control angles and control angular velocities to form a stable closed loop within a limit cycle, thereby allowing the biped walking robot to balance itself while changing its supporting foot and thus to safely walk without falling down.