Time-derivative estimation by backward differencing. JointAccelerationBackwardDifference uses backward differencing to estimate the second time derivative of the joint state
Time-derivative estimation by backward differencing. JointJerkBackwardDifference uses backward differencing to estimate the third time derivative of the joint state
Implementation of joint limits task map. Note: we dont want to always stay at the centre of the joint range, be lazy as long as the joint is not too close to the low/high limits
Time-derivative estimation by backward differencing. JointVelocityBackwardDifference uses backward differencing to estimate the first time derivative of the joint state
Joint Velocity Limit taskmap for time-indexed problems. Penalisations of joint velocity limit violation within a specified percentage of the velocity limit
Points end-effector to look at a given target by aligning end-effector z-axis with the target. Looks at a target point by penalizing the vector which defines the orthogonal projection onto a defined line in the end-effector frame
Manipulability measure. The manipulability measure for a robot at a given joint configuration indicates dexterity, that is, how isotropic the robot's motion is with respect to the task space motion. The measure is high when the manipulator is capable of equal motion in all directions and low when the manipulator is close to a singularity. This task map implements Yoshikawa's manipulability measure
that is based on the shape of the velocity ellipsoid where is the manipulator Jacobian matrix.. The task map is expressed by
Time-derivative estimation by backward differencing. JointAccelerationBackwardDifference uses backward differencing to estimate the second time derivative of the joint state
Time-derivative estimation by backward differencing. JointJerkBackwardDifference uses backward differencing to estimate the third time derivative of the joint state
Implementation of joint limits task map. Note: we dont want to always stay at the centre of the joint range, be lazy as long as the joint is not too close to the low/high limits
Time-derivative estimation by backward differencing. JointVelocityBackwardDifference uses backward differencing to estimate the first time derivative of the joint state
Joint Velocity Limit taskmap for time-indexed problems. Penalisations of joint velocity limit violation within a specified percentage of the velocity limit
Points end-effector to look at a given target by aligning end-effector z-axis with the target. Looks at a target point by penalizing the vector which defines the orthogonal projection onto a defined line in the end-effector frame
Manipulability measure. The manipulability measure for a robot at a given joint configuration indicates dexterity, that is, how isotropic the robot's motion is with respect to the task space motion. The measure is high when the manipulator is capable of equal motion in all directions and low when the manipulator is close to a singularity. This task map implements Yoshikawa's manipulability measure
that is based on the shape of the velocity ellipsoid where is the manipulator Jacobian matrix.. The task map is expressed by
![\[ m(x) = \sqrt{J(x)J(x)^T} \]](form_17.png)
is the manipulator Jacobian matrix.. The task map is expressed by ![\[ \phi(x) := -m(x). \]](form_19.png)