Systems and methods for determining 6DoF correction trajectories in compensating movement of a treatment target in a patient

1. A computer-implemented method comprising, by at least one processor:

receiving a starting end-effector position in six degrees-of-freedom (6DoF) associated with an end-effector at each one of a plurality of cycles, a starting target position in 6DoF associated with a clinical target, and a target destination position in 6DoF associated with a desired target position, the target destination position corresponding to a position in space receiving targeted treatment from a treatment delivery device, wherein movement of the end-effector effects movement of the clinical target;

determining a destination end-effector position in 6DoF associated with the end-effector, wherein positioning the end-effector on the destination end-effector position would cause the target to be positioned on the target destination position;

calculating, at each one of the plurality of cycles in a real-time manner and using a quasi-Newtonian Limited-Broyden-Fletcher-Goldfarb-Shannon (L-BFGS) algorithm, a 6DoF trajectory between the starting end-effector position associated with the end-effector and the destination end-effector position associated with the end-effector, wherein the trajectory comprises a plurality of discrete or continuous steps and wherein the calculating the 6DoF trajectory comprises solving an optimization problem to minimize a correction distance and a time to the target destination position that is subjected to actuator mechanical constraints and system dynamical constraints, the optimization problem determining a next end-effector position associated with a next step in the trajectory;

transmitting, to a mechanical device controlling movement of the end-effector, one or more signals causing the end-effector to move from the starting end-effector position to the destination end-effector position along the determined trajectory,

wherein the mechanical device comprises a kinematics robot system having a plurality of actuators, and

wherein the one or more signals cause actuators to change the length of one or more of the plurality of actuators; and

utilizing a motion stabilization method to:

detect a motion of the clinical target away from the destination end-effector position; and

transmit, to the kinematics robot system, one or more additional signals to modify, in real-time, a length of the one or more of the plurality of actuators to reposition the clinical target to the desired end-effector position.

2. The method of claim 1 , wherein the trajectory comprises a plurality of discrete steps and wherein the calculating the 6DoF trajectory comprises determining the discrete steps by interpolating between the starting target position and the target destination position.

3. The method of claim 1 , wherein the transmitting comprises:

transmitting, to a mechanical device controlling movement of the end-effector, one or more signals causing the end-effector to move from the starting end-effector position to the next end-effector position,

wherein the method further comprises repeating the determining the next end-effector position and transmitting signals causing the end-effector to move to the next end-effector position so as to cause the end-effector to move from the starting end-effector position to the destination end-effector position along the determined trajectory in a step-by-step manner.

4. The method of claim 1 , wherein the calculating the 6DoF trajectory comprises minimizing a time integral of a target position error along the target trajectory, wherein the target position error comprises a difference between the starting target position and the destination target position.

5. The method of claim 1 , wherein the trajectory comprises a shortest-path trajectory between the starting end-effector position and the destination end-effector position.

6. The method of claim 1 , wherein the trajectory comprises a target error steepest-descent trajectory between the starting end-effector position and the destination end-effector position.

7. The method of claim 1 , wherein the trajectory comprises a weighted combination of a short-path trajectory and a steepest-descent trajectory between the starting end-effector position and the destination end-effector position.

8. A system, comprising:

a mechanical device coupled to an end-effector; and

a memory and at least one processor coupled to the memory, the processor configured to:

receive a starting end-effector position in six degrees-of-freedom (6DoF) associated with an end-effector at each one of a plurality of cycles, a starting target position in 6DoF associated with a clinical target, and a target destination position in 6DoF associated with a desired target position, the target destination position corresponding to a position in space receiving targeted treatment from a treatment delivery device, wherein movement of the end-effector effects movement of the clinical target;

determine a destination end-effector position in 6DoF associated with the end-effector, wherein positioning the end-effector on the destination end-effector position would cause the target to be positioned on the target destination position;

calculate, at each one of the plurality of cycles in a real-time manner and using a quasi-Newtonian Limited-Broyden-Fletcher-Goldfarb-Shannon (L-BFGS) algorithm, a 6DoF trajectory between the starting end-effector position associated with the end-effector and the destination end-effector position associated with the end-effector, wherein the trajectory comprises a plurality of discrete or continuous steps and wherein the calculating the 6DoF trajectory comprises solving an optimization problem to minimize a correction distance and a time to the target destination position that is subjected to actuator mechanical constraints and system dynamical constraints, the optimization problem determining a next end-effector position associated with a next step in the trajectory;

transmit, to a mechanical device controlling movement of the end-effector, one or more signals causing the end-effector to move from the starting end-effector position to the destination end-effector position along the determined trajectory,

wherein the mechanical device comprises a kinematics robot system having a plurality of actuators, and

wherein the one or more signals cause actuators to change the length of one or more of the plurality of actuators; and

utilize a motion stabilization method to:

detect a motion of the clinical target away from the destination end-effector position; and

transmit, to the kinematics robot system, one or more additional signals to modify, in real-time, a length of the one or more of the plurality of actuators to reposition the clinical target to the desired end-effector position.

9. The system of claim 8 , wherein the trajectory comprises a plurality of discrete steps and wherein the calculating the 6DoF trajectory comprises determining the discrete steps by interpolating between the starting target position and the target destination position.

10. The system of claim 8 , wherein, the interpolation or optimization methods are based on the starting end-effector position, the starting target position, and the target destination position, and the interpolation or optimization methods optimize an end-effector motion.

11. The system of claim 8 , wherein to transmit the one or more signals the processor is further configured to:

transmit, to a mechanical device controlling movement of the end-effector, one or more signals causing the end-effector to move from the starting end-effector position to the next end-effector position,

wherein the processor is further configured to repeatedly determine the next end-effector position and transmit signals causing the end-effector to move to the next end-effector position so as to cause the end-effector to move from the starting end-effector position to the destination end-effector position along the determined trajectory in a step-by-step manner.

12. A non-transitory computer-readable device having instructions stored thereon that, when executed by at least one computing device, causes the at least one computing device to perform operations comprising:

receiving a starting end-effector position in six degrees-of-freedom (6DoF) associated with an end-effector at each one of a plurality of cycles, a starting target position in 6DoF associated with a clinical target, and a target destination position in 6DoF associated with a desired target position, the target destination position corresponding to a position in space receiving targeted treatment from a treatment delivery device, wherein movement of the end-effector effects movement of the clinical target;

determining a destination end-effector position in 6DoF associated with the end-effector, wherein positioning the end-effector on the destination end-effector position would cause the target to be positioned on the target destination position;

calculating, at each one of the plurality of cycles in a real-time manner and using a quasi-Newtonian Limited-Broyden-Fletcher-Goldfarb-Shannon (L-BFGS) algorithm, a 6DoF trajectory between the starting end-effector position associated with the end-effector and the destination end-effector position associated with the end-effector, wherein the trajectory comprises a plurality of discrete or continuous steps and wherein the calculating the 6DoF trajectory comprises solving an optimization problem to minimize a correction distance and a time to the target destination position that is subjected to actuator mechanical constraints and system dynamical constraints, the optimization problem determining a next end-effector position associated with a next step in the trajectory;

transmitting, to a mechanical device controlling movement of the end-effector, one or more signals causing the end-effector to move from the starting end-effector position to the destination end-effector position along the determined trajectory,

wherein the mechanical device comprises a kinematics robot system having a plurality of actuators, and

wherein the one or more signals cause actuators to change the length of one or more of the plurality of actuators; and

utilizing a motion stabilization method to:

detect a motion of the clinical target away from the destination end-effector position; and

transmit, to the kinematics robot system, one or more additional signals to modify, in real-time, a length of the one or more of the plurality of actuators to reposition the clinical target to the desired end-effector position.

13. A computer-implemented method comprising, by at least one processor:

receiving a starting device position in six degrees-of-freedom (6DoF) associated with a treatment delivery device at each one of a plurality of cycles and a target position in 6DoF associated with a clinical target, the starting device position corresponding to a position in space receiving targeted treatment from a treatment delivery device;

determining a destination device position in 6DoF associated with the treatment delivery device, wherein positioning the treatment delivery device on the destination device position would cause the treatment to be delivered to the target position;

calculating, at each one of the plurality of cycles in a real-time manner and using a quasi-Newtonian Limited-Broyden-Fletcher-Goldfarb-Shannon (L-BFGS) algorithm, a 6DoF trajectory between the starting device position and the destination device position, wherein the trajectory comprises a plurality of discrete or continuous steps and wherein the calculating the 6DoF trajectory comprises solving an optimization problem to minimize a correction distance and a time to the target destination position that is subjected to actuator mechanical constraints and system dynamical constraints, the optimization problem determining a next end-effector position associated with a next step in the trajectory;

transmitting, to a mechanical device controlling movement of the treatment delivery device, one or more signals causing the treatment delivery device to move from the starting device position to the destination device position along the determined trajectory,

wherein the mechanical device comprises a kinematics robot system having a plurality of actuators, and

wherein the one or more signals cause actuators to change the length of one or more of the plurality of actuators; and

utilizing a motion stabilization method to:

detect a motion of the clinical target away from the destination end-effector position; and

transmit, to the kinematics robot system, one or more additional signals to modify, in real-time, a length of the one or more of the plurality of actuators to reposition the clinical target to the desired end-effector position.