Legged Robot Gait Optimization Using Environment Warping
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Solution Overview
Problem
Contact-aware gait trajectory optimization for legged robots over curved terrain is challenging due to high-dimensional search spaces and the likelihood of finding local minima, leading to sub-optimal solutions and computational inefficiencies.
Innovation Solution
An environment warping approach transforms the curved ambient space into a flat warped space using a locally injective mapping function, allowing for contact-aware trajectory optimization under geometrical, physical, and force constraints, with decision variables parameterized using high-order spines and optimized in the warped space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If contact-aware trajectory optimization is performed in ambient space, then the trajectory can be generated for curved terrain, but the optimization procedure fails to find optimal solutions and falls into local minima
Solution Approach 1:
The patent transforms the optimization problem from ambient space to warped space by introducing a coordinate transformation dimension. This changes the search space geometry, converting curved terrain constraints in ambient space into flat terrain constraints in warped space, thereby eliminating local minima and improving optimization reliability
Solution Approach 2:
The patent applies parameter transformation through the mapping function that converts ambient space coordinates to warped space coordinates. By changing the parameterization of the search space, the optimization problem becomes well-conditioned with convex constraints, preventing convergence to local minima
2Adaptability or versatility
If complex multi-variable search space optimization is used for gait trajectory generation, then comprehensive terrain constraints can be considered, but the procedure fails to find solutions or falls into sub-optimal local minima
Solution Approach 1:
The patent transforms complex terrain constraints in ambient space into simplified flat terrain constraints in warped space through coordinate transformation. This parameter change maintains adaptability to complex terrains while improving optimization reliability by converting the problem into a well-conditioned form
Solution Approach 2:
The mapping function serves as an intermediary transformation between ambient space and warped space. It mediates the complex terrain constraints by translating them into simpler constraints in the warped coordinate system, enabling reliable optimization while preserving terrain adaptability
3Shape
If trajectory optimization is performed in ambient space, then the original terrain geometry is preserved, but computational efficiency decreases and local minima are encountered
Solution Approach 1:
The patent introduces a warped space dimension where terrain geometry is transformed into a flat representation. This dimensional transformation preserves the essential terrain features through the mapping function while enabling computationally efficient optimization without local minima
Solution Approach 2:
By changing the coordinate parameters from ambient space to warped space, the patent transforms the optimization landscape into a convex form. This parameter transformation maintains terrain geometry fidelity through the mapping relationship while dramatically improving computational efficiency
Data Source
AI summary
An environment warping approach is implemented to improve a robustness of contact-aware robot trajectory optimization by a change of coordinates from an ambient space to a flat space. The disclosed method warps the ambient space of a curved terrain to a warped space with a flat terrain using a optimized mapping function. A contact-aware trajectory optimization procedure is then formulated in the warped space under a set of geometrical and physical constraints with decision variables pulled back from the ambient space to the warped flat space. The decision variables are parameterized using high-order spines with a set of control parameters which are optimized in the warped space in order to generate the gait trajectory in the ambient space. For example, an objective function and constraint functions from the ambient space are pushed back to the warped space while force and rotational variables are pushed forward from the warped space to the ambient space. Such an approach, in comparison to implementations involving optimization within the ambient space only achieves a higher success rate in fining optical solutions.