Mobile Robot Motion State Estimation via Polyhedron Projection
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Solution Overview
Problem
Existing methods struggle to generate stable desired motions for mobile robots moving in three-dimensional environments with varied action patterns, as they fail to effectively manage contact reaction forces and maintain balance, leading to difficulties in estimating the possible existence region of overall motion state quantities.
Innovation Solution
A device and method utilizing polyhedron projection processing through multi-parametric linear programming to estimate the possible existence region of specific state quantities such as the overall center-of-gravity position, translational motion state, and rotational motion state, which satisfies contact reaction force constraint conditions by projecting a convex polyhedron into a subspace representing these state quantities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional ZMP-based motion generation methods are used, then motion generation is simple on flat floors, but the method fails to generate stable motions in three-dimensional environments with varied action patterns
Solution Approach 1:
The invention transitions from static ZMP constraints to dynamic constraints that adapt to varying contact configurations. By formulating constraints based on contact reaction forces and using polyhedral projection methods, the system dynamically adjusts motion generation to suit different action patterns (walking, climbing, jumping) while maintaining reliability through mathematical guarantees of constraint satisfaction.
Solution Approach 2:
The invention changes the fundamental parameters of motion generation by replacing ZMP position constraints with contact reaction force constraints. This parameter transformation enables the system to handle diverse three-dimensional motions by expressing constraints in terms of forces and moments at contacting portions, allowing adaptation to various environments while maintaining stability through force-based control.
2Reliability
If contact reaction force constraints are enforced for stable motion in varied action patterns, then motion stability improves, but computational complexity increases
Solution Approach 1:
The invention segments the high-dimensional constraint satisfaction problem into manageable parts by projecting the convex polyhedron of contact reaction forces onto lower-dimensional subspaces. This segmentation allows the system to handle complex force constraints by breaking them down into independent linear programming problems for each contacting portion, reducing computational complexity while maintaining motion stability.
Solution Approach 2:
The invention replaces complex mechanical balance calculations with mathematical optimization methods. By substituting traditional dynamic model-based approaches with polyhedral projection and linear programming techniques, the system achieves stable motion generation through computational efficiency, transforming a mechanically complex problem into a mathematically tractable optimization task.
3Measurement precision
If polyhedron projection processing is used to estimate possible existence region, then estimation accuracy improves, but processing time increases
Solution Approach 1:
The invention applies partial projection by focusing computational effort on estimating the possible existence region of specific state quantities (such as center of gravity position or contact forces) rather than computing the complete high-dimensional polyhedron. This partial action approach maintains estimation accuracy for critical parameters while significantly reducing processing time by avoiding unnecessary computations in less relevant dimensions.
Solution Approach 2:
The invention performs preliminary projection of the convex polyhedron onto key subspaces before detailed motion planning. By pre-computing the possible existence regions of important state quantities, the system prepares accurate estimation data in advance, enabling faster real-time motion generation while maintaining high estimation accuracy through the use of pre-projected constraint boundaries.
Data Source
AI summary
An arithmetic processing unit 40 estimates a possible existence region of a specific state quantity by performing polyhedron projection processing for finding a projection region obtained by projecting a convex polyhedron to a subspace representing the specific state quantity, where the convex polyhedron is within a space configured with the contact reaction forces of a plurality of contacting portions (13, 23) of a mobile robot 1 and the specific state quantity as variable components and where the convex polyhedron is specified by a mechanical relation between the contact reaction forces and the specific state quantity and by a linear inequality representing a contact reaction force constraint condition.