Robotic Manipulation Control Under Contact and Friction Uncertainty
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Solution Overview
Problem
Robotic systems face challenges in motion planning and control due to uncertainty in contact forces and coefficients of friction, making it difficult to incorporate constraints effectively for complex manipulation tasks.
Innovation Solution
A system and method using a Stochastic Discrete-time Linear Complementarity Model (SDLCM) with complementarity constraints, formulating a chance constrained optimization problem, and employing Sample Average Approximation (SAA) and an important-particle algorithm for covariance control to manage uncertainty and optimize control inputs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If motion planning and control incorporate contact constraints for complex manipulation tasks, then manipulation dexterity is improved, but uncertainty propagation becomes challenging
Solution Approach 1:
The system segments the manipulation task into discrete time steps and models contacts as separate complementarity constraints at each step. This allows uncertainty to be propagated step-by-step through the SDLCM framework rather than attempting to propagate it through the entire manipulation sequence at once, reducing the overall complexity.
Solution Approach 2:
The patent introduces complementarity variables as intermediary elements that mediate between the contact constraints and the state evolution. These variables serve as a bridge that allows the system to handle contact uncertainty in a structured way, enabling tractable propagation of uncertainty through the manipulation sequence.
2Productivity
If the system models contact-rich manipulation using complementarity constraints, then contact efficiency is improved, but controller design becomes difficult due to implicit state-complementarity relationships
Solution Approach 1:
The system employs a discrete-time dynamic model where the state and complementarity variables evolve together through the SDLCM framework. This dynamic formulation captures the implicit relationships between state and complementarity variables while maintaining computational tractability through the structured propagation approach.
Solution Approach 2:
The patent transforms the controller design problem by changing the parameter representation to include both state variables and complementarity variables in the propagation process. This parameter transformation allows the implicit relationships to be handled systematically rather than requiring direct inversion of the coupled system.
3Reliability
If chance constraints are formulated to constrain state within a particular set with certain probability, then reliability is improved, but computational complexity increases
Solution Approach 1:
The system performs preliminary sampling of uncertainty to generate particles that represent possible trajectories. By pre-computing these particles and their propagated states, the system converts the complex chance-constrained optimization into a more tractable form that can be solved using the particle-based approach.
Solution Approach 2:
The patent replaces the traditional mechanical approach to handling chance constraints with a computational particle-based method. Instead of directly solving the probabilistic constraints through complex optimization, the system uses Monte Carlo sampling and particle propagation to approximate and satisfy the chance constraints.
Data Source
AI summary
The present disclosure provides a system and a method for controlling an operation of a manipulation system. The method comprises formulating an optimization problem based on a Stochastic Discrete-time Linear Complementarity Model (SDLCM) of a manipulation task, and a sample average approximation; solving the formulated optimization problem using an important-particle algorithm to compute an optimal state trajectory, an optimal feedforward control trajectory, an optimal complementarity variable trajectory, a state feedback gain, and a complementarity feedback gain; collecting, measurements indicative of a current state trajectory and a current complementarity variable trajectory; determining an online control input based on the optimal feedforward control trajectory, a deviation of the current state trajectory from the optimal state trajectory, a deviation of the current complementarity variable trajectory from the optimal complementarity variable trajectory, the state feedback gain, and the complementarity feedback gain; and controlling actuators of the manipulation system according to the online control input.