Methods, apparatus, systems and articles of manufacture are disclosed to improve resource utilization for binary tree structures. An example apparatus to improve resource utilization for field programmable gate array (FPGA) resources includes a computation determiner to identify a computation capability value associated with the FPGA resources, a k-ary tree builder to build a first k-ary tree having a number of k-ary nodes equal to the computation capability value, and an FPGA memory controller to initiate collision computation by transferring the first k-ary tree to a first memory of the FPGA resources.

The invention relates to a robot, a robot control system, and a method for controlling a robot. The robot comprises a movable, multi-membered robot structure (102) that can be driven by means of actuators (101), at least one marked structural element S being defined on the movable robot structure (102), with at least one point P.sub.S marked on the structural element S. The robot is designed such that, in an input mode, it learns positions POS.sub.PS of the point PS and/or poses of the structural element S in a work space of the robot, the user exerting an input force F.sub.EING on the movable robot structure in order to move the structural element S, which is conveyed to the point P.sub.S as F.sub.EING,PS, and/or to the structural element S as torque M.sub.EING,S. A control device (103) of the robot is designed such that, in the input mode, the actuators (101) are controlled on the basis of a pre-defined space-fixed virtual 3D grid that at least partially fills the work space, such that the structural element S is moved with a pre-defined force F.sub.GRID (POS.sub.PS), according to the current position POS.sub.PS of the point P.sub.S in the 3D grid, to the adjacent grid point of the 3D grid or in a grid point space defined around the adjacent grid point of the 3D grid, the point P.sub.S of the structural element S remaining on said adjacent grid point or in said grid point space in the event of the following holding true: |F.sub.EING,PS|<|F.sub.GRID(POS.sub.PS) and/or, in the input mode, the actuators (101) are controlled on the basis of a pre-defined virtual discrete 3D orientation space O, where the 3D orientation space O=: (α.sub.i, β.sub.j, γ.sub.k) where i=1, 2, . . . , I, j=1, 2, . . . J, k=1, 2, . . . , K is defined or can be defined by a pre-defined angle α.sub.i, β.sub.j, γ.sub.k, in such a way that the structural element S is moved with a pre-defined torque)(SO ROM according to the current orientation OR.sub.S of the structural element, towards the adjacent discrete orientation of the 3D orientation space O=: (α.sub.i, β.sub.j, γ.sub.k), S, the structural element remaining in said adjacent discrete orientation of the 3D orientation space O in the event that the following holds true: |M.sub.EING,S|<|M.sub.O(OR.sub.S).

Methods, apparatus, systems and articles of manufacture are disclosed to improve resource utilization for binary tree structures. An example apparatus to improve resource utilization for field programmable gate array (FPGA) resources includes a computation determiner to identify a computation capability value associated with the FPGA resources, a k-ary tree builder to build a first k-ary tree having a number of k-ary nodes equal to the computation capability value, and an FPGA memory controller to initiate collision computation by transferring the first k-ary tree to a first memory of the FPGA resources.

A method of performing motion planning for a robot in a workspace discretized into workspace elements includes generating or receiving a first model and determining a first set comprising one or more workspace elements that are at least partially in collision with the first model for each of a plurality of states and the respective transition(s) between those states. A first mapping is generated including information regarding the first set and the respective states and transition(s). The method further includes generating or receiving a second model extending from the first model and determining a second set including one or more further workspace elements, additional to those in the first set, that are at least partially in collision with the second model for each of the plurality of states and transitions between those states. A second mapping including information regarding said second set and the respective states and transition(s) is generated.

The invention relates to a robot, a robot control system, and a method for controlling a robot. The robot comprises a movable, multi-membered robot structure (102) that can be driven by means of actuators (101), at least one marked structural element S being defined on the movable robot structure (102), with at least one point P.sub.S marked on the structural element S. The robot is designed such that, in an input mode, it learns positions POS.sub.PS of the point PS and/or poses of the structural element S in a work space of the robot, the user exerting an input force F.sub.EING on the movable robot structure in order to move the structural element S, which is conveyed to the point P.sub.S as F.sub.EING,PS, and/or to the structural element S as torque M.sub.EING,S. A control device (103) of the robot is designed such that, in the input mode, the actuators (101) are controlled on the basis of a pre-defined space-fixed virtual 3D grid that at least partially fills the work space, such that the structural element S is moved with a pre-defined force F.sub.GRID (POS.sub.PS), according to the current position POS.sub.PS of the point P.sub.S in the 3D grid, to the adjacent grid point of the 3D grid or in a grid point space defined around the adjacent grid point of the 3D grid, the point P.sub.S of the structural element S remaining on said adjacent grid point or in said grid point space in the event of the following holding true: |F.sub.EING,PS|<|F.sub.GRID(POS.sub.PS) and/or, in the input mode, the actuators (101) are controlled on the basis of a pre-defined virtual discrete 3D orientation space O, where the 3D orientation space O=: (.sub.i, .sub.j, .sub.k) where i=1, 2, . . . , I, j=1, 2, . . . J, k=1, 2, . . . , K is defined or can be defined by a pre-defined angle .sub.i, .sub.j, .sub.k, in such a way that the structural element S is moved with a pre-defined torque)(SO ROM according to the current orientation OR.sub.S of the structural element, towards the adjacent discrete orientation of the 3D orientation space O=: (.sub.i, .sub.j, .sub.k), S, the structural element remaining in said adjacent discrete orientation of the 3D orientation space O in the event that the following holds true: |M.sub.EING,S|<|M.sub.O(OR.sub.S).