MECH572-lecture11.ppt

文档介绍：MECH572Introduction To Robotics
Lecture 11
Dept. Of Mechanical Engineering
Review
Recursive Inverse Dynamics
Inverse Dynamics – Known joint pute joint torques
1) Outward Recursion – putation
pute
From 0 to n, recursively based on geometrical and differential relationship associated with each link.
2) Inward Recursion – putation
Compute wrench wi based on wi+1 and kinematic quantities obtained from 1)
From n+1 to 0, recursively using Newton-Euler equation
Review
The Natural pliment
Each link – 6-DOF; Within the system – 1-DOF
5-DOF constrained
Kinematic Constraint equation

T : Natural plement (Twist Shape Function)
Review
Natural plement (cont'd)
Use T in the Newton-Euler Equation, the system equation of motion es:
where
Consistent with the result obtained from Euler-Lagrange equation
Generalized inertia matrix
Active force
Dissipative force
Gravitational force
Vector of Coriolis and centrifugal force
Natural plement
Constraint Equations & Twist-Shape Matrix
1) Angular velocity Constraint
Ei : Cross-product matrix of ei

2) Linear Velocity Constraints
ci = ci-1+ i-1 + i
Differentiate:

Oi-1
Oi
O
Ci-1
Ci
ci-1
c
i-1
i
Oi+1
Natural plement
Constraint Equations & Twist Shape Matrix – R Joint
Equations () and () pertaining to the first link:
Natural plement
Constraint Equations & Twist Shape Matrix – R Joint

6n 6n matrix
Natural plement
Constraint Equations & Twist Shape Matrix – R Joint
Define partial Jacobian

6 n matrix with its element defined as

Mapping the first i joint rates to ti of the ith link
Natural plement
Constraint Equations & Twist Shape Matrix – R Joint
Natural plement
Constraint Equation and Twist Shape Matrix – R Joint
Easy to verify

Recall