Autonomous correction of alignment error in a master-slave robotic system

A method of correcting an alignment error between an end effector of a tool associated with a slave and a master actuator associated with a master in a master-slave robotic system in which an orientation of the end effector is remotely controlled by an orientation of the master actuator by producing and transmitting control signals at the master for controlling the slave, the method comprising:

• causing a processor associated with the master to receive master actuator orientation signals (RMCURR) representing the orientation of the master actuator relative to a master reference frame;
• causing the processor to generate end effector orientation signals (REENEW) representing the end effector orientation relative to a slave reference frame, in response to:
• said master actuator orientation signals (RMCURR);
• and
• master-slave misalignment signals (RΔ), representing a product of previously saved values of said master actuator orientation signals (RMCURR) and said end effector orientation signals (REENEW);
• causing the processor to produce control signals based on said end effector orientation signals, for transmission from the master to the slave;
• causing the processor to receive an enablement signal for selectively enabling said control signals to be transmitted from the master to the slave whereby the master transmits said control signals to the slave when said enablement signal is active and does not transmit said control signals to the slave when said enablement signal is not active and such that when said enablement signal is active, changes in the orientation of the master actuator cause corresponding changes in the orientation of the end effector and such that when said enablement signal is not active, changes in the orientation of the master actuator do not cause corresponding changes in the orientation of the end effector;
• when said enablement signal transitions from said not active state to said active state, causing the processor to:
• compute the master-slave misalignment signals (RΔ) as a difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the misalignment signals representing a difference in physical alignment between the tool and the master relative to their respective reference frames, the difference based on a difference rotation matrix that carries the end effector orientation signals into the master actuator orientation signals according to the relation:
• REE_TO_MASTER=REENEW−1RMCURR
• Where:
• REENEW−1 is an inverse matrix of the end effector orientation signal REENEW represented by a 3×3 matrix;
• and
• RMCURR is the master actuator orientation signal at a current time step represented by a 3×3 matrix;
• causing the processor to determine an angle of rotation associated with the difference rotation matrix according to the relation:
• φEE_TO_MASTER=a cos(0.5 trace(REE_TO_MASTER)−1);
• causing the processor to detect a second difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the second difference representing the difference in physical alignment between the tool and the master relative to their respective reference frames;
• and
• in response to detecting said second difference, causing the processor to adjust said master-slave misalignment signals (RΔ) to reduce the alignment difference to satisfy an alignment criterion so that subsequent generations of said end effector orientation signals (REENEW) cause said control signals to cause said tool to be physically aligned with said master within the alignment criterion.

An apparatus for correcting an alignment error between an end effector of a tool associated with a slave and a master actuator associated with a master in a master-slave robotic system in which an orientation of the end effector is remotely controlled by an orientation of the master actuator by producing and transmitting control signals at the master for controlling the slave, the apparatus comprising:

• computing means associated with the master, the computing means for:
• receiving master actuator orientation signals (RMCURR) representing the orientation of the master actuator relative to a master reference frame;
• generating end effector orientation signals (REENEW) representing the end effector orientation relative to a slave reference frame, in response to:
• said master actuator orientation signals (RMCURR);
• master base orientation signals (RMBASE) representing previous-saved values of said master actuator orientation signals (RMCURR);
• and
• slave base orientation signals (REEBASE) representing previous-saved values of said end effector orientation signals (REENEW);
• producing control signals based on said end effector orientation signals, for transmission from the master to the slave;
• receiving an enablement signal for selectively enabling said control signals to be transmitted from the master to the slave whereby the master transmits said control signals to the slave when said enablement signal is active and does not transmit said control signals to the slave when said enablement signal is not active and such that when said enablement signal is active, changes in the orientation of the master actuator cause corresponding changes in the orientation of the end effector and such that when said enablement signal is not active, changes in the orientation of the master actuator do not cause corresponding changes in the orientation of the end effector;
• responsive to a transition of the enablement signal from said not active state to said active state, for:
• saving said values of said master actuator orientation signals (RMCURR) as said master base orientation signals (RMBASE) to create said previous-saved values of said master actuator orientation signals (RMCURR);
• and
• saving said values of said end effector orientation signals (REENEW) as said slave base orientation signals (REEBASE) to create said previous-saved values of said end effector orientation signals (REENEW);
• detecting a difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the difference representing a difference in physical alignment between the tool and the master relative to their respective reference frames, wherein detecting the difference comprises computing a difference rotation matrix that carries the end effector orientation signals into the master actuator orientation signals according to the relation:
• REE_TO_MASTER=REENEW−1RMCURR
• Where:
• REENEW−1 is an inverse matrix of the end effector orientation signal REENEW represented by a 3×3 matrix;
• and
• RMCURR is the master actuator orientation signal at a current time step represented by a 3×3 matrix;
• adjusting said saved slave base orientation signals (REEBASE) to ultimately have the same values as said saved master base orientation (RMBASE) values so that subsequent generations of said end effector orientation signals (REENEW) cause said control signals to cause said tool to satisfy an alignment criterion, in response to detecting said difference;
• and
• determining an angle of rotation associated with the difference rotation matrix according to the relation:
• φEE_TO_MASTER=a cos(0.5 trace(REE_TO_MASTER)−1).

An apparatus for correcting an alignment error between an end effector of a tool associated with a slave and a master actuator associated with a master in a master-slave robotic system in which an orientation of the end effector is remotely controlled by an orientation of the master actuator by producing and transmitting control signals at the master for controlling the slave, the apparatus comprising:

• computing means associated with the master, the computing means for:
• receiving master actuator orientation signals (RMCURR) representing the orientation of the master actuator relative to a master reference frame;
• generating end effector orientation signals (REENEW) representing the end effector orientation relative to a slave reference frame, in response to:
• said master actuator orientation signals (RMCURR);
• and
• master-slave misalignment signals (RΔ), representing a product of previously saved values of said master actuator orientation signals (RMCURR) and said end effector orientation signals (REENEW);
• producing control signals based on said end effector orientation signals, for transmission from the master to the slave;
• receiving an enablement signal for selectively enabling said control signals to be transmitted from the master to the slave whereby the master transmits said control signals to the slave when said enablement signal is active and does not transmit said control signals to the slave when said enablement signal is not active and such that when said enablement signal is active, changes in the orientation of the master actuator cause corresponding changes in the orientation of the end effector and such that when said enablement signal is not active, changes in the orientation of the master actuator do not cause corresponding changes in the orientation of the end effector;
• responsive to a transition of the enablement signal from said not active state to said active state, for:
• computing the master-slave misalignment signals (RΔ) as a difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the misalignment signals representing a difference in physical alignment between the tool and the master relative to their respective reference frames, the difference based on a difference rotation matrix that carries the end effector orientation signals into the master actuator orientation signals according to the relation:
• REE_TO_MASTER=REENEW−1RMCURR
• Where:
• REENEW−1 is an inverse matrix of the end effector orientation signal REENEW represented by a 3×3 matrix;
• and
• RMCURR is the master actuator orientation signal at a current time step represented by a 3×3 matrix;
• determining an angle of rotation associated with the difference rotation matrix according to the relation:
• φEE_TO_MASTER=a cos(0.5 trace(REE_TO_MASTER)−1);
• detecting a second difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the second difference representing the difference in physical alignment between the tool and the master relative to their respective reference frames;
• and
• responsive to detecting said second difference, for adjusting said master-slave misalignment signals (RΔ) to reduce the alignment difference to satisfy an alignment criterion so that subsequent generations of said end effector orientation signals (REENEW) cause said control signals to cause said tool to be physically aligned with said master within the alignment criterion.

An apparatus for correcting an alignment error between an end effector of a tool associated with a slave and a master actuator associated with a master in a master-slave robotic system in which an orientation of the end effector is remotely controlled by an orientation of the master actuator by producing and transmitting control signals at the master for controlling the slave, the apparatus comprising:

• a processor associated with the master operably configured to:
• receive master actuator orientation signals (RMCURR) representing the orientation of the master actuator relative to a master reference frame;
• generate end effector orientation signals (REENEW) representing the end effector orientation relative to a slave reference frame, in response to:
• said master actuator orientation signals (RMCURR);
• master base orientation signals (RMBASE) representing previous-saved values of said master actuator orientation signals (RMCURR);
• and
• slave base orientation signals (REEBASE) representing previous-saved values of said end effector orientation signals (REENEW);
• produce control signals based on said end effector orientation signals, for transmission from the master to the slave;
• receive an enablement signal for selectively enabling said control signals to be transmitted from the master to the slave whereby the master transmits said control signals to the slave when said enablement signal is active and does not transmit said control signals to the slave when said enablement signal is not active and such that when said enablement signal is active, changes in the orientation of the master actuator cause corresponding changes in the orientation of the end effector and such that when said enablement signal is not active, changes in the orientation of the master actuator do not cause corresponding changes in the orientation of the end effector;
• when said enablement signal transitions from said not active state to said active state:
• save said values of said master actuator orientation signals (RMCURR) as said master base orientation signals (RMBASE) to create said previous-saved values of said master actuator orientation signals (RMCURR);
• and
• save said values of said end effector orientation signals (REENEW) as said slave base orientation signals (REEBASE) to create said previous-saved values of said end effector orientation signals (REENEW);
• detect a difference, between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the difference representing a difference in physical alignment between the tool and the master relative to their respective reference frames, the processor configured to detect the difference by computing a difference rotation matrix that carries the end effector orientation signals into the master actuator orientation signals according to the relation:
• REE_TO_MASTER=REENEW−1RMCURR
• Where:
• REENEW−1 is an inverse matrix of the end effector orientation signal REENEW represented by a 3×3 matrix;
• and
• RMCURR is the master actuator orientation signal at a current time step represented by a 3×3 matrix;
• determine an angle of rotation associated with the difference rotation matrix according to the relation:
• φEE_TO_MASTER=a cos(0.5 trace(REE_TO_MASTER)−1);
• and
• adjust said saved slave base orientation signals (REEBASE) to ultimately have the same values as said saved master base orientation (RMBASE) values so that subsequent generations of said end effector orientation signals (REENEW) cause said control signals to cause said tool to satisfy an alignment criterion, in response to detecting said difference.

An apparatus for correcting an alignment error between an end effector of a tool associated with a slave and a master actuator associated with a master in a master-slave robotic system in which an orientation of the end effector is remotely controlled by an orientation of the master actuator by producing and transmitting control signals at the master for controlling the slave, the apparatus comprising:

• a processor associated with the master operably configured to:
• receive master actuator orientation signals (RMCURR) representing the orientation of the master actuator relative to a master reference frame;
• generate end effector orientation signals (REENEW) representing the end effector orientation relative to a slave reference frame, in response to:
• said master actuator orientation signals (RMCURR);
• and
• master-slave misalignment signals (RΔ), representing a product of previously saved values of said master actuator orientation signals (RMCURR) and said end effector orientation signals (REENEW);
• produce control signals based on said end effector orientation signals, for transmission from the master to the slave;
• receive an enablement signal for selectively enabling said control signals to be transmitted from the master to the slave whereby the master transmits said control signals to the slave when said enablement signal is active and does not transmit said control signals to the slave when said enablement signal is not active and such that when said enablement signal is active, changes in the orientation of the master actuator cause corresponding changes in the orientation of the end effector and such that when said enablement signal is not active, changes in the orientation of the master actuator do not cause corresponding changes in the orientation of the end effector;
• in response to a transition of the enablement signal from said not active state to said active state:
• compute the master-slave misalignment signals (RΔ) as a difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the misalignment signals representing a difference in physical alignment between the tool and the master relative to their respective reference frames, the difference based on a difference rotation matrix that carries the end effector orientation signals into the master actuator orientation signals according to the relation:
• REE_TO_MASTER=REENEW−1RMCURR
• Where:
• REENEW−1 is an inverse matrix of the end effector orientation signal REENEW represented by a 3×3 matrix;
• and
• RMCURR is the master actuator orientation signal at a current time step represented by a 3×3 matrix;
• to determine an angle of rotation associated with the difference rotation matrix according to the relation:
• φEE_TO_MASTER=a cos(0.5 trace(REE_TO_MASTER)−1);
• detect a second difference between the master actuator orientation signals (RMCURR) and the end effector orientation signals (REENEW), the second difference representing the difference in physical alignment between the tool and the master relative to their respective reference frames;
• and
• responsive to detecting said second difference, adjusting said master-slave misalignment signals (RΔ) to reduce the alignment difference to satisfy an alignment criterion so that subsequent generations of said end effector orientation signals (REENEW) cause said control signals to cause said tool to be physically aligned with said master within the alignment criterion.