Robotic Manipulator Task Null Space for Local Minima Avoidance
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Solution Overview
Problem
Existing methods for controlling robotic manipulators do not effectively account for task-specific properties, such as physical interactions with objects, and can converge to local minima, leading to suboptimal task execution and loss of control during physical interactions.
Innovation Solution
A method that involves determining a task null space by discretizing it into observation points, using a computing unit to execute a kinematic or dynamic model of the robotic manipulator, and optimizing a target function to maximize or minimize a predetermined variable, thereby improving task execution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing control methods are used for robotic manipulators, then the control system is simpler, but the task execution is suboptimal and can converge to local minima
Solution Approach 1:
The control space is segmented into task null space and robot null space, allowing independent optimization of each. The task null space is discretized into observation points, enabling systematic exploration without overwhelming complexity. This segmentation resolves the contradiction by structuring the control problem into manageable parts that improve reliability without requiring complete redesign of the entire control system.
Solution Approach 2:
The patent performs preliminary discretization of the task null space into observation points before executing the optimization algorithm. This preliminary action transforms the continuous optimization problem into a discrete evaluation of finite points, which prevents convergence to local minima while keeping the computational complexity manageable through pre-structured observation points.
2Reliability
If optimization algorithms are applied to improve task execution, then task-specific properties are considered, but the algorithm can converge to local minima instead of global minima
Solution Approach 1:
The continuous task null space is segmented into discrete observation points, transforming the optimization problem from continuous to discrete. This segmentation allows the algorithm to evaluate multiple distinct configurations without getting trapped in local minima, as the discrete nature of observation points provides a structured search space that avoids continuous local optima traps.
Solution Approach 2:
The patent evaluates a finite number of observation points that may exceed the minimum necessary for task completion. By considering more candidate configurations than strictly required, the system increases the probability of finding the global optimum while maintaining computational feasibility through the finite discretization approach.
3Adaptability or versatility
If the robotic manipulator uses redundant degrees of freedom, then more task possibilities are available, but the control system becomes much more complex
Solution Approach 1:
The patent extracts the task null space from the complete configuration space by identifying variations that do not affect task execution. This extraction separates the redundant degrees of freedom into a distinct subspace that can be optimized independently, reducing control complexity while preserving adaptability. The robot null space is similarly extracted and optimized separately, allowing systematic handling of redundancy without overwhelming complexity.
Solution Approach 2:
The patent transforms the control problem by adding the dimension of null space optimization to the traditional task space control. By introducing the task null space as an additional dimension for optimization, the system exploits redundant degrees of freedom to improve task execution while maintaining a structured approach that prevents control system complexity from becoming unmanageable.
4Force
If impedance control is used during physical interaction, then contact force control is improved, but desired rigidity cannot be generated across the kinematic chain
Solution Approach 1:
The patent introduces the task null space as an intermediary between the end effector contact forces and the kinematic chain configuration. By optimizing configurations within the task null space, the system mediates between contact force requirements and kinematic rigidity, allowing impedance control to function effectively while maintaining desired rigidity across the entire kinematic chain through coordinated null space optimization.
Data Source
AI summary
A system and method of controlling a robotic manipulator, wherein the method includes: providing information regarding a task to be executed; determining a task null space from the provided information via a computing unit, the task null space being characterized by a set of variations of a kinematic variable of the end effector, with all of which variations the task is capable of being executed; establishing observation points by discretizing the task null space into a finite number of the variations via the computing unit; executing an optimization method to optimize a predefined target function, including execution of a model of the robotic manipulator for each of the observation points; and controlling the robotic manipulator to assume an optimal variation of the end effector determined according to a result of the optimization method.