Closed-Kinematics Manipulator Motion Planning Under Collision Constraints
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Solution Overview
Problem
Current motion planning methods for robots with closed kinematics face challenges in generating collision-free trajectories, particularly with probabilistic methods that result in high computational times and non-deterministic outcomes, while optimization-based methods require complex formulation and are not adaptable to changing environments.
Innovation Solution
Formulating collision-free motion planning as a dynamic optimization problem that includes cost functions, inequality constraints for collision avoidance, and equality constraints for maintaining closed kinematics, solved numerically to produce deterministic and adaptable trajectories.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If probabilistic methods (PRM or RRT) are used for motion planning, then motion paths can be found, but computational time becomes very high and trajectories are non-deterministic
Solution Approach 1:
The patent replaces probabilistic sampling-based methods with a deterministic optimization-based approach. By formulating motion planning as a dynamic optimization problem with cost functions and constraints, the system achieves reliable collision-free trajectories with predictable computational time, eliminating the randomness and high computational burden of probabilistic methods.
Solution Approach 2:
The patent changes the fundamental approach from probabilistic sampling to deterministic optimization by adjusting key parameters: using cost functions to evaluate trajectories, implementing inequality constraints for collision avoidance, and applying equality constraints for closed kinematics. This parameter transformation enables both reliability and computational efficiency.
2Loss of time
If optimization-based methods are used to generate deterministic trajectories, then computational time is predictable, but the formulation of the optimization problem becomes complex
Solution Approach 1:
The patent segments the complex optimization problem into manageable components: a cost function for trajectory evaluation, inequality constraints for collision avoidance, equality constraints for closed kinematics, and boundary conditions for start and end states. This segmentation makes the formulation systematic and tractable while maintaining deterministic computational time.
Solution Approach 2:
The patent creates a universal optimization framework that can handle multiple requirements simultaneously through a unified mathematical formulation. The dynamic optimization problem with constraints serves as a multi-functional tool that addresses collision avoidance, kinematics maintenance, and trajectory optimization in a single coherent system.
3Reliability
If closed kinematics constraints are enforced, then manipulator contact is maintained, but freedom of movement is restricted
Solution Approach 1:
The patent applies dynamics by formulating closed kinematics as time-varying equality constraints in the optimization problem. This allows the manipulator to dynamically adapt its motion while maintaining contact, transforming static kinematic constraints into dynamic optimization constraints that preserve both reliability and movement flexibility.
Solution Approach 2:
The patent changes the representation of closed kinematics from rigid positional constraints to dynamic optimization constraints that evolve with time. By incorporating time as a parameter in the equality constraints, the system maintains manipulator contact while allowing adaptive movement throughout the trajectory.
Data Source
AI summary
A method is described for collision-free motion planning of a first manipulator with closed kinematics. The method includes defining a dynamic optimization problem, solving the optimization problem using a numerical approach, and determining a first movement path for the first manipulator based on the solution of the optimization problem. The dynamic optimization problem includes a cost function that weights states and control variables of the first manipulator, a dynamic that defines states and control variables of the first manipulator as a function of time, and at least one inequality constraint for a distance to collisions. Furthermore, the optimization problem includes at least one equality constraint for the closed kinematics.