Gait Generation for Legged Robots Using Quadratic Programming
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Solution Overview
Problem
Conventional techniques for generating gaits for legged mobile robots do not adequately consider the mechanical restrictions of joints and actuators, leading to potential overextension or restriction of joint displacements and velocities, which can impair the smoothness and accuracy of the robot's operation.
Innovation Solution
A gait generating device that determines desired joint displacements and velocities by using a Jacobian matrix and quadratic programming to minimize an evaluation function within constraints defined by joint operation restrictions, ensuring that joint velocities and displacements fall within permissible ranges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Power
If conventional gait generation techniques are used to generate desired gaits for legged mobile robots, then the robot can achieve the desired translational momentum vector and angular momentum vector, but the joint displacement amounts and temporal change rates may exceed the variable ranges defined by mechanical restrictions
Solution Approach 1:
The invention performs preliminary action by determining upper and lower limits of joint velocities and displacement amounts before generating the gait. By pre-calculating the variable ranges based on mechanical restrictions and using these limits as constraints in the gait generation process, the system ensures that the desired gait will not cause joints to exceed their operational limits, thus preventing reliability issues before they occur.
Solution Approach 2:
The invention applies parameter changes by transforming the physical constraints (joint displacement amounts and temporal change rates) into mathematical parameters (upper and lower limits of joint velocities). These parameterized constraints are then integrated into the gait generation algorithm, allowing the system to dynamically adjust the gait parameters while respecting the mechanical restrictions of the robot.
2Reliability
If joint displacement amounts or temporal change rates are forcibly restricted to the upper or lower limit of the variable range, then the mechanical restrictions are satisfied, but the smoothness of robot operation is impaired
Solution Approach 1:
The invention applies dynamics by generating a gait that is dynamically adapted to the robot's mechanical restrictions. Rather than using static, fixed restrictions that degrade performance, the system dynamically calculates appropriate velocity limits based on the current gait parameters and mechanical constraints, then generates a gait trajectory that smoothly satisfies both the desired motion and the joint limitations.
Solution Approach 2:
The invention uses parameter changes to transform the hard constraints into soft constraints through parameterized velocity limits. By expressing the mechanical restrictions as upper and lower bounds on joint velocities and incorporating these as optimization constraints, the system can find gait solutions that respect the limits while maintaining smooth operation, avoiding the discontinuities that would result from hard clipping.
3Reliability
If the generable form of the operational target is restricted to a limited form that can reliably satisfy the restriction conditions, then joint mechanical restrictions are satisfied, but the flexibility in generating desired gaits is reduced
Solution Approach 1:
The invention applies parameter changes by transforming the mechanical restrictions into parameterized velocity limits that can be flexibly adjusted. Rather than restricting the operational target to a limited form, the system parameterizes the constraints and integrates them into the gait generation optimization, allowing a wide range of gait forms to be generated as long as they satisfy the parameterized velocity bounds.
Solution Approach 2:
The invention uses dynamics to create an adaptive gait generation system that can handle various operational requirements. By dynamically calculating velocity limits based on the desired gait parameters and mechanical constraints, the system maintains reliability while preserving adaptability to different gait patterns and operational scenarios.
Data Source
AI summary
A gait generating device 32 includes a desired particular-site motion velocity value determining unit 45 that uses a quadratic evaluation function having a particular-site motion velocity vector ↑Vb as a variable and a linear matrix inequality having ↑Vb as a variable to sequentially determine, as a desired value ↑Vb_cmd2 of ↑Vb, a value of ↑Vb that can minimize the value of the evaluation function within a range in which a restriction condition that the linear matrix inequality holds is satisfied, by arithmetic processing according to a solution method for a quadratic programming problem. The device then integrates ↑Vb_cmd2 to sequentially determine desired values of the position and posture of the particular site (the body) 2 of the robot 1. The linear matrix inequality is set to satisfy a condition restricting the operations of the joints between the particular site 2 and the distal portion of each leg link 3.