Robotic Manipulation Under Uncertain Contact With Chance Constraints
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current robotic manipulation systems struggle with unreliable optimization and control due to stochastic complementarity constraints arising from frictional interaction uncertainties, leading to infeasibility in trajectory optimization problems.
Innovation Solution
A robotic system employing a chance constrained optimization formulation, specifically Mixed-Integer Quadratic Programming with Chance Constraints (MIQPCC), to address stochastic discrete-time complementarity systems (SDLCS) by imposing joint chance constraints on state and complementarity constraints, converting hard constraints into soft constraints through cost functions and expected residual minimization penalties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LCP-based contact models are used for trajectory optimization, then contact dynamics can be modeled, but stochastic complementarity constraints cause infeasibility in optimization
Solution Approach 1:
The patent introduces chance constraints as an intermediary mechanism between the stochastic complementarity constraints and the optimization solver. By formulating chance-constrained LCP models, the patent transforms hard complementarity constraints into probabilistic constraints with specified violation probabilities, enabling feasible solutions under uncertainty while maintaining the essential contact dynamics modeling capability
Solution Approach 2:
The patent changes the mathematical formulation parameters by transforming deterministic complementarity constraints into chance-constrained formulations. This involves modifying the constraint satisfaction criteria from absolute satisfaction to probabilistic satisfaction with controlled violation rates, fundamentally altering how the optimization problem handles contact uncertainties
Data Source
Figure 1
Figure 2
Figure 3
AI summary
A robotic system for manipulating an object with a robotic manipulator is provided. The robotic system is configured to collect a digital representation of a task for manipulating the object; solve a robust control problem to optimize a sequence of control forces to be applied by the robotic manipulator to change a state of the object, where an evolution of the state of the object is governed by a stochastic complementarity system modeling the task with a predefined probability. The robust control problem optimizes a cost function to generate the sequence of control forces performing the task subject to joint chance constraints including a first chance constraint on the state of the object being manipulated and a second chance constraint on stochastic complementarity constraints modeling manipulation of the object. The robotic system is further configured to control the manipulation of the object based on the sequence of control forces.