Operational Space Control for Humanoid Robots Using Orthogonal Projections
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Solution Overview
Problem
Current operational space control methods for robotic systems, particularly underactuated and constrained systems like humanoid robots, are complex and inefficient due to the need for explicit consideration of constraint forces and inertia matrices, limiting their application and accuracy.
Innovation Solution
The use of orthogonal projections to simplify operational space dynamics formulations, allowing for control signals to be generated without explicit consideration of constraint forces or dynamic consistency, and the application of dynamically consistent null space forces to compensate for passive degrees of freedom, resulting in a unified control approach for both constrained and unconstrained systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If operational space control methods explicitly consider constraint forces and inertia matrices, then control accuracy is improved, but computational complexity and system efficiency deteriorate
Solution Approach 1:
The patent extracts and eliminates the need for explicit constraint force calculations and inertia matrix computations from the operational space control formulation. By using orthogonal projections, the method removes these computationally intensive elements while preserving the essential control functionality, thus reducing computational complexity without sacrificing control accuracy.
Solution Approach 2:
The patent substitutes the traditional mechanical dynamics approach (based on Newton-Euler or Lagrangian mechanics requiring inertia matrices and constraint forces) with a projection-based mathematical formulation. This substitution replaces complex mechanical calculations with simpler linear algebra operations, significantly reducing computational burden while maintaining control precision.
2Reliability
If operational space control methods explicitly consider constraint forces, then dynamic consistency is improved, but control simplicity and ease of operation deteriorate
Solution Approach 1:
The patent implements a control formulation where the system self-maintains dynamic consistency through orthogonal projections without requiring explicit calculation or active management of constraint forces. The projection operator automatically ensures that control actions remain consistent with system constraints, eliminating the need for complex force compensation mechanisms and simplifying the control implementation.
3Adaptability or versatility
If operational space formulations are applied to humanoid robots with floating base and environmental contacts, then task dynamics control is improved, but system complexity and difficulty of manufacture deteriorate
Solution Approach 1:
The patent develops a universal operational space control formulation using orthogonal projections that can handle multiple task types (manipulation, balance, locomotion) and various constraint conditions (environmental contacts, passive joints) within a single unified framework. This universal approach eliminates the need for separate control formulations for different task scenarios, reducing overall system complexity while maintaining versatility.
Data Source
AI summary
An operational space control solution is provided for rigid-body dynamical systems such as humanoid or legged robots. The solution includes an operational space controller that decomposes rigid body dynamics into task space dynamics and null space dynamics. Then, for systems that are fully actuated and have constraints, the controller provides control signals defining task space torques and null space torques for each actuator (e.g., a motor for a rotary joint between two rigid links). In some embodiments, a minimum torque vector is determined such that the controller is a minimum-torque operational space controller. For systems that are underactuated, task and null space dynamics are again considered, and underactuation is addressed by using null space forces to indirectly apply torque at passive degrees of freedom such as at active joints to create task-irrelevant motion that moves passive joints to facilitate task performance by the robot or rigid-body dynamical system.