Patent Publication Number: US-2022219916-A1

Title: A robotic system with packing mechanism

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation of U.S. patent application Ser. No. 15/931,530, filed May 13, 2020, issued as U.S. Pat. No. ______, which is a continuation of U.S. patent application Ser. No. 16/428,645, filed May 31, 2019, issued as U.S. Pat. No. 10,696,493, both of which are incorporated by reference herein in their entirety. 
     This application contains subject matter related to U.S. patent application Ser. No. 16/428,714, filed May 31, 2019, issued as U.S. Pat. No. 10,679,379, titled “A ROBOTIC SYSTEM WITH DYNAMIC PACKING MECHANISM,” and is incorporated herein by reference in its entirety. 
     This application contains subject matter related to U.S. patent application Ser. No. 16/428,809, filed May 31, 2019, issued as U.S. Pat. No. 10,618,172, titled “A ROBOTIC SYSTEM WITH ERROR DETECTION AND DYNAMIC PACKING MECHANISM,” and is incorporated herein by reference in its entirety. 
     This application contains subject matter related U.S. patent application Ser. No. 16/428,843, filed May 31, 2019, issued as U.S. Pat. No. 10,696,494, titled “ROBOTIC SYSTEM FOR PROCESSING PACKAGES ARRIVING OUT OF SEQUENCE,” and is incorporated herein by reference in its entirety. 
     This application contains subject matter related to U.S. patent application Ser. No. 16/428,870, filed May 31, 2019, issued as U.S. Pat. No. 10,647,528, titled “ROBOTIC SYSTEM FOR PALLETIZING PACKAGES USING REAL-TIME PLACEMENT SIMULATION,” and is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present technology is directed generally to robotic systems and, more specifically, to systems, processes, and techniques for packing objects. 
     BACKGROUND 
     With their ever-increasing performance and lowering cost, many robots (e.g., machines configured to automatically/autonomously execute physical actions) are now extensively used in many fields. Robots, for example, can be used to execute various tasks (e.g., manipulate or transfer an object through space) in manufacturing and/or assembly, packing and/or packaging, transport and/or shipping, etc. In executing the tasks, the robots can replicate human actions, thereby replacing or reducing the human involvement that would otherwise be required to perform dangerous or repetitive tasks. 
     However, despite the technological advancements, robots often lack the sophistication necessary to duplicate human sensitivity and/or adaptability required for executing more complex tasks. For example, robots often lack the granularity of control and flexibility in the executed actions to account for deviations or uncertainties that may result from various real-world factors. Accordingly, there remains a need for improved techniques and systems for controlling and managing various aspects of the robots to complete the tasks despite the various real-world factors. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of an example environment in which a robotic system with a 3-dimensional packing mechanism may operate. 
         FIG. 2  is a block diagram illustrating the robotic system in accordance with one or more embodiments of the present technology. 
         FIG. 3A  is an illustration of discretized objects in accordance with one or more embodiments of the present technology. 
         FIG. 3B  is an illustration of discretized packing platform in accordance with one or more embodiments of the present technology. 
         FIG. 3C  is an illustration of a placement planning process in accordance with one or more embodiments of the present technology. 
         FIGS. 4A-4C  are illustrations of stacking rules in accordance with one or more embodiments of the present technology. 
         FIG. 5A  is an illustration of an example stacking plan in accordance with one or more embodiments of the present technology. 
         FIG. 5B  is an illustration of a stacking sequence in accordance with one or more embodiments of the present technology. 
         FIG. 6  is a flow diagram for operating the robotic system of  FIG. 1  in accordance with one or more embodiments of the present technology. 
     
    
    
     DETAILED DESCRIPTION 
     Systems and methods for robotic systems with packing mechanisms are described herein. A robotic system (e.g., an integrated system of devices that executes one or more designated tasks) configured in accordance with some embodiments provides enhanced packing and storage efficiency by deriving optimal storage locations for objects and stacking them accordingly. 
     Traditional systems use offline packing simulators to predetermine packing sequences/arrangements. The traditional packing simulators process object information (e.g., case shapes/sizes) for a predetermined or estimated set of cases to generate packing plans. Once determined, the packing plans dictate and/or require specific placement locations/poses of the objects at destinations (e.g., pallets, bins, cages, boxes, etc.), predefined sequences for the placement, and/or predetermined motion plans. From the predetermined packing plans, the traditional packing simulators may derive source requirements (e.g., sequences and/or placements for the objects) that match or enable the packing plans. Because the packing plans are developed offline in traditional systems, the plans are independent of actual packing operations/conditions, object arrivals, and/or other system implementations. Accordingly, the overall operation/implementation will require the received packages (e.g., at the starting/pick up location) to follow fixed sequences that matches the predetermined packing plans. As such, traditional systems cannot adapt to real-time conditions and/or deviations in the received packages (e.g., different sequence, location, and/or orientation), unanticipated errors (e.g., collisions and/or lost pieces), real-time packing requirements (e.g., received orders), and/or other real-time factors. 
     Further, because traditional systems group and pack objects according to rigid predetermined plans/sequences, they require all objects at a source location to either (1) have a same dimension/type and/or (2) arrive according to a known sequence. For example, the traditional systems would require the objects to arrive (via, e.g., conveyor) at a pickup location according to a fixed sequence. Also, for example, the traditional systems would require the objects at the pickup location to be placed at designated locations according to a predetermined pose. As such, traditional systems require one or more operations to order and/or place the objects at the source (i.e., before the packing operation) according to the predetermined sequence/arrangement. Often, the traditional systems require a sequence buffer, which costs upwards of one million US dollars, to order and/or place the objects at the source according to the predetermined sequence/pose. 
     In contrast, the robotic system described herein can generate the packing plans during system operation. The robotic system can generate a real-time and/or dynamic packing plan during the system operation based on various real-time conditions. Real-time conditions can include currently existing or ongoing conditions, such as actual source sequences/locations/poses of objects, object conditions and/or requirements, placement requirements, and/or other real-time factors. The robotic system can generate the packing plans in real-time, such as in response to a triggering event (e.g., a received order/request, a shipping schedule, and/or an operator input), according to current/ongoing conditions and factors at the time of the packing plan processing. In some embodiments, the packing plans can be dynamically (e.g., after initially starting one or more operations, such as the actual packing operation, begins) generated and/or adjusted, such as in response to a corresponding event (e.g., a re-evaluation timing, a packing/manipulation error, such as a collision or a lost piece, and/or occurrence of other dynamic conditions). 
     Unlike the traditional systems, the robotic system described herein can generate the placement plans in real-time according to current/live conditions (e.g., source sequences/locations/poses of objects, object conditions and/or requirements, etc.). In some embodiments, the robotic system can generate the packing plan based on a discretization mechanism (e.g., a process, a circuit, a function, and/or a routine). For example, the robotic system can use the discretization mechanism to describe physical sizes/shapes of objects and/or target locations according to a discretization unit (i.e., one discrete area/space). The robotic system can generate discretized object profiles that use the discretization units to describe the expected objects and/or discretized destination profiles that describe the target location (e.g., surface on top of the pallet and/or a space/bottom surface inside a bin/case/box). Accordingly, the robotic system can transform continuous real-world space/area into computer-readable digital information. Further, the discretized data can allow a reduction in computational complexity for describing package footprint and for comparing various package placements. For example, package dimensions can correspond to integer numbers of discretization units, which lead to easier mathematical computations, instead of real-world decimal number. 
     In some embodiments, the robotic system can generate the packing plan based on determining object groupings. The object groupings can be based on object descriptions, such as customer-specified priorities, object fragility measure (e.g., support weight limitations), object weight, object height, object type, and/or other aspects of the objects. The robotic system can use the object groupings to generate and evaluate 2-dimensional (2D) placement plans that include one or more object groupings. The robotic system can select the 2D placement plans that satisfy one or more conditions/rules and translate the selected 2D placement plans into three-dimensional (3D) mapping results. The 3D mapping results can describe the heights of the 2D placement plans, such as according to height measurements of the objects included in the 2D placement plans and their relative locations within the layer. The robotic system can evaluate the 3D mapping results to vertically order/sequence to generate the 3D placement plans that include the vertical sequence for the 2D placement plans. In some embodiments, the robotic system can generate the 2D/3D placement plans for objects in an initial state (e.g., before any objects are placed at the destination zone) and/or for objects remaining in a non-packed state (e.g., after one or more objects have been placed at the destination zone). Details regarding the object grouping and the placement plans are described below. 
     The robotic system described below can utilize simplified and stream-lined processing architecture/sequence for real-time implementation. For example, the robotic system (via, e.g., a consumer computing device, such as a desk top, a server, etc.) can generate the packing plan based on real-time need (e.g., received order) and/or real-time availability (e.g., shipping manifesto of incoming objects and/or currently accessible objects) without utilizing the traditional sequencer and simulator. When utilized in an offline context, such as to replace the traditional sequencers and simulators, the robotic system can provide the offline packing plans using a simpler and cheaper solution. 
     Accordingly, the robotic system can improve efficiency, speed, and accuracy for packing the objects based on adapting to the real-time conditions. For example, the system described herein can generate the placement plans that match/address the currently need (e.g., received orders), the current status (e.g., location, orientation, and/or quantity/availability) of packages, and/or the real-time status of previously stacked/placed packages. As such, the robotic system can receive and pack packages that are in various different/unexpected quantities, locations, orientations, and/or sequences. 
     Further, the robotic system can reduce overall costs by eliminating the one or more operations, machines (e.g., sequence buffers), and/or human assistance that would be necessary in traditional systems to order or place the objects at the source and/or for the packing operation (e.g., for error handling). By generating the packing plan according to the existing package states (e.g., quantity, location, and/or orientation), the robotic system eliminates the need to reorganize or sequence the packages, along with the associated machines/human operations, to meet the requirements of traditional systems. 
     In the following description, numerous specific details are set forth to provide a thorough understanding of the presently disclosed technology. In other embodiments, the techniques introduced here can be practiced without these specific details. In other instances, well-known features, such as specific functions or routines, are not described in detail in order to avoid unnecessarily obscuring the present disclosure. References in this description to “an embodiment,” “one embodiment,” or the like mean that a particular feature, structure, material, or characteristic being described is included in at least one embodiment of the present disclosure. Thus, the appearances of such phrases in this specification do not necessarily all refer to the same embodiment. On the other hand, such references are not necessarily mutually exclusive either. Furthermore, the particular features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments. It is to be understood that the various embodiments shown in the figures are merely illustrative representations and are not necessarily drawn to scale. 
     Several details describing structures or processes that are well-known and often associated with robotic systems and subsystems, but that can unnecessarily obscure some significant aspects of the disclosed techniques, are not set forth in the following description for purposes of clarity. Moreover, although the following disclosure sets forth several embodiments of different aspects of the present technology, several other embodiments can have different configurations or different components than those described in this section. Accordingly, the disclosed techniques can have other embodiments with additional elements or without several of the elements described below. 
     Many embodiments or aspects of the present disclosure described below can take the form of computer- or processor-executable instructions, including routines executed by a programmable computer or processor. Those skilled in the relevant art will appreciate that the disclosed techniques can be practiced on computer or processor systems other than those shown and described below. The techniques described herein can be embodied in a special-purpose computer or data processor that is specifically programmed, configured, or constructed to execute one or more of the computer-executable instructions described below. Accordingly, the terms “computer” and “processor” as generally used herein refer to any data processor and can include Internet appliances and handheld devices (including palm-top computers, wearable computers, cellular or mobile phones, multi-processor systems, processor-based or programmable consumer electronics, network computers, mini computers, and the like). Information handled by these computers and processors can be presented at any suitable display medium, including a liquid crystal display (LCD). Instructions for executing computer- or processor-executable tasks can be stored in or on any suitable computer-readable medium, including hardware, firmware, or a combination of hardware and firmware. Instructions can be contained in any suitable memory device, including, for example, a flash drive and/or other suitable medium. 
     The terms “coupled” and “connected,” along with their derivatives, can be used herein to describe structural relationships between components. It should be understood that these terms are not intended as synonyms for each other. Rather, in particular embodiments, “connected” can be used to indicate that two or more elements are in direct contact with each other. Unless otherwise made apparent in the context, the term “coupled” can be used to indicate that two or more elements are in either direct or indirect (with other intervening elements between them) contact with each other, or that the two or more elements cooperate or interact with each other (e.g., as in a cause-and-effect relationship, such as for signal transmission/reception or for function calls), or both. 
     Suitable Environments 
       FIG. 1  is an illustration of an example environment in which a robotic system  100  with a packing mechanism may operate. The robotic system  100  can include and/or communicate with one or more units (e.g., robots) configured to execute one or more tasks. Aspects of the packing mechanism can be practiced or implemented by the various units. 
     For the example illustrated in  FIG. 1 , the robotic system  100  can include an unloading unit  102 , a transfer unit  104  (e.g., a palletizing robot and/or a piece-picker robot), a transport unit  106 , a loading unit  108 , or a combination thereof in a warehouse or a distribution/shipping hub. Each of the units in the robotic system  100  can be configured to execute one or more tasks. The tasks can be combined in sequence to perform an operation that achieves a goal, such as to unload objects from a truck or a van and store them in a warehouse or to unload objects from storage locations and prepare them for shipping. For another example, the task can include placing the objects on a target location (e.g., on top of a pallet and/or inside a bin/cage/box/case). As described below, the robotic system can derive plans (e.g., placement locations/orientations, sequence for transferring the objects, and/or corresponding motion plans) for placing and/or stacking the objects. Each of the units can be configured to execute a sequence of actions (e.g., operating one or more components therein) to execute a task. 
     In some embodiments, the task can include manipulation (e.g., moving and/or reorienting) of a target object  112  (e.g., one of the packages, boxes, cases, cages, pallets, etc. corresponding to the executing task) from a start location  114  to a task location  116 . For example, the unloading unit  102  (e.g., a devanning robot) can be configured to transfer the target object  112  from a location in a carrier (e.g., a truck) to a location on a conveyor belt. Also, the transfer unit  104  can be configured to transfer the target object  112  from one location (e.g., the conveyor belt, a pallet, or a bin) to another location (e.g., a pallet, a bin, etc.). For another example, the transfer unit  104  (e.g., a palletizing robot) can be configured to transfer the target object  112  from a source location (e.g., a pallet, a pickup area, and/or a conveyor) to a destination pallet. In completing the operation, the transport unit  106  can transfer the target object  112  from an area associated with the transfer unit  104  to an area associated with the loading unit  108 , and the loading unit  108  can transfer the target object  112  (by, e.g., moving the pallet carrying the target object  112 ) from the transfer unit  104  to a storage location (e.g., a location on the shelves). Details regarding the task and the associated actions are described below. 
     For illustrative purposes, the robotic system  100  is described in the context of a shipping center; however, it is understood that the robotic system  100  can be configured to execute tasks in other environments/for other purposes, such as for manufacturing, assembly, packaging, healthcare, and/or other types of automation. It is also understood that the robotic system  100  can include other units, such as manipulators, service robots, modular robots, etc., not shown in  FIG. 1 . For example, in some embodiments, the robotic system  100  can include a depalletizing unit for transferring the objects from cage carts or pallets onto conveyors or other pallets, a container-switching unit for transferring the objects from one container to another, a packaging unit for wrapping the objects, a sorting unit for grouping objects according to one or more characteristics thereof, a piece-picking unit for manipulating (e.g., for sorting, grouping, and/or transferring) the objects differently according to one or more characteristics thereof, or a combination thereof. 
     Suitable System 
       FIG. 2  is a block diagram illustrating the robotic system  100  in accordance with one or more embodiments of the present technology. In some embodiments, for example, the robotic system  100  (e.g., at one or more of the units and/or robots described above) can include electronic/electrical devices, such as one or more processors  202 , one or more storage devices  204 , one or more communication devices  206 , one or more input-output devices  208 , one or more actuation devices  212 , one or more transport motors  214 , one or more sensors  216 , or a combination thereof. The various devices can be coupled to each other via wire connections and/or wireless connections. For example, the robotic system  100  can include a bus, such as a system bus, a Peripheral Component Interconnect (PCI) bus or PCI-Express bus, a HyperTransport or industry standard architecture (ISA) bus, a small computer system interface (SCSI) bus, a universal serial bus (USB), an IIC (I2C) bus, or an Institute of Electrical and Electronics Engineers (IEEE) standard 1394 bus (also referred to as “Firewire”). Also, for example, the robotic system  100  can include bridges, adapters, processors, or other signal-related devices for providing the wire connections between the devices. The wireless connections can be based on, for example, cellular communication protocols (e.g., 3G, 4G, LTE, 5G, etc.), wireless local area network (LAN) protocols (e.g., wireless fidelity (WIFI)), peer-to-peer or device-to-device communication protocols (e.g., Bluetooth, Near-Field communication (NFC), etc.), Internet of Things (IoT) protocols (e.g., NB-IoT, LTE-M, etc.), and/or other wireless communication protocols. 
     The processors  202  can include data processors (e.g., central processing units (CPUs), special-purpose computers, and/or onboard servers) configured to execute instructions (e.g. software instructions) stored on the storage devices  204  (e.g., computer memory). In some embodiments, the processors  202  can be included in a separate/stand-alone controller that is operably coupled to the other electronic/electrical devices illustrated in  FIG. 2  and/or the robotic units illustrated in  FIG. 1 . The processors  202  can implement the program instructions to control/interface with other devices, thereby causing the robotic system  100  to execute actions, tasks, and/or operations. 
     The storage devices  204  can include non-transitory computer-readable mediums having stored thereon program instructions (e.g., software). Some examples of the storage devices  204  can include volatile memory (e.g., cache and/or random-access memory (RAM)) and/or non-volatile memory (e.g., flash memory and/or magnetic disk drives). Other examples of the storage devices  204  can include portable memory drives and/or cloud storage devices. 
     In some embodiments, the storage devices  204  can be used to further store and provide access to processing results and/or predetermined data/thresholds. For example, the storage devices  204  can store master data  252  that includes descriptions of objects (e.g., boxes, cases, and/or products) that may be manipulated by the robotic system  100 . In one or more embodiments, the master data  252  can include a dimension, a shape (e.g., templates for potential poses and/or computer-generated models for recognizing the object in different poses), a color scheme, an image, identification information (e.g., bar codes, quick response (QR) codes, logos, etc., and/or expected locations thereof), an expected weight, other physical/visual characteristics, or a combination thereof for the objects expected to be manipulated by the robotic system  100 . In some embodiments, the master data  252  can include manipulation-related information regarding the objects, such as a center-of-mass (CoM) location on each of the objects, expected sensor measurements (e.g., for force, torque, pressure, and/or contact measurements) corresponding to one or more actions/maneuvers, or a combination thereof. Also, for example, the storage devices  204  can store object tracking data  254 . In some embodiments, the object tracking data  254  can include a log of scanned or manipulated objects. In some embodiments, the object tracking data  254  can include imaging data (e.g., a picture, point cloud, live video feed, etc.) of the objects at one or more locations (e.g., designated pickup or drop locations and/or conveyor belts). In some embodiments, the object tracking data  254  can include locations and/or orientations of the objects at the one or more locations. 
     The communication devices  206  can include circuits configured to communicate with external or remote devices via a network. For example, the communication devices  206  can include receivers, transmitters, modulators/demodulators (modems), signal detectors, signal encoders/decoders, connector ports, network cards, etc. The communication devices  206  can be configured to send, receive, and/or process electrical signals according to one or more communication protocols (e.g., the Internet Protocol (IP), wireless communication protocols, etc.). In some embodiments, the robotic system  100  can use the communication devices  206  to exchange information between units of the robotic system  100  and/or exchange information (e.g., for reporting, data gathering, analyzing, and/or troubleshooting purposes) with systems or devices external to the robotic system  100 . 
     The input-output devices  208  can include user interface devices configured to communicate information to and/or receive information from human operators. For example, the input-output devices  208  can include a display  210  and/or other output devices (e.g., a speaker, a haptics circuit, or a tactile feedback device, etc.) for communicating information to the human operator. Also, the input-output devices  208  can include control or receiving devices, such as a keyboard, a mouse, a touchscreen, a microphone, a user interface (UI) sensor (e.g., a camera for receiving motion commands), a wearable input device, etc. In some embodiments, the robotic system  100  can use the input-output devices  208  to interact with the human operators in executing an action, a task, an operation, or a combination thereof. 
     The robotic system  100  can include physical or structural members (e.g., robotic manipulator arms) that are connected at joints for motion (e.g., rotational and/or translational displacements). The structural members and the joints can form a kinetic chain configured to manipulate an end-effector (e.g., the gripper) configured to execute one or more tasks (e.g., gripping, spinning, welding, etc.) depending on the use/operation of the robotic system  100 . The robotic system  100  can include the actuation devices  212  (e.g., motors, actuators, wires, artificial muscles, electroactive polymers, etc.) configured to drive or manipulate (e.g., displace and/or reorient) the structural members about or at a corresponding joint. In some embodiments, the robotic system  100  can include the transport motors  214  configured to transport the corresponding units/chassis from place to place. 
     The robotic system  100  can include the sensors  216  configured to obtain information used to implement the tasks, such as for manipulating the structural members and/or for transporting the robotic units. The sensors  216  can include devices configured to detect or measure one or more physical properties of the robotic system  100  (e.g., a state, a condition, and/or a location of one or more structural members/joints thereof) and/or of a surrounding environment. Some examples of the sensors  216  can include accelerometers, gyroscopes, force sensors, strain gauges, tactile sensors, torque sensors, position encoders, etc. 
     In some embodiments, for example, the sensors  216  can include one or more imaging devices  222  (e.g., visual and/or infrared cameras, 2D and/or 3D imaging cameras, distance measuring devices such as lidars or radars, etc.) configured to detect the surrounding environment. The imaging devices  222  can generate representations of the detected environment, such as digital images and/or point clouds, that may be processed via machine/computer vision (e.g., for automatic inspection, robot guidance, or other robotic applications). As described in further detail below, the robotic system  100  (via, e.g., the processors  202 ) can process the digital image and/or the point cloud to identify the target object  112  of  FIG. 1 , the start location  114  of  FIG. 1 , the task location  116  of  FIG. 1 , a pose of the target object  112 , a confidence measure regarding the start location  114  and/or the pose, or a combination thereof. 
     For manipulating the target object  112 , the robotic system  100  (via, e.g., the various circuits/devices described above) can capture and analyze an image of a designated area (e.g., a pickup location, such as inside the truck or on the conveyor belt) to identify the target object  112  and the start location  114  thereof. Similarly, the robotic system  100  can capture and analyze an image of another designated area (e.g., a drop location for placing objects on the conveyor, a location for placing objects inside the container, or a location on the pallet for stacking purposes) to identify the task location  116 . For example, the imaging devices  222  can include one or more cameras configured to generate images of the pickup area and/or one or more cameras configured to generate images of the task area (e.g., drop area). Based on the captured images, as described below, the robotic system  100  can determine the start location  114 , the task location  116 , the associated poses, a packing/placement plan, a transfer/packing sequence, and/or other processing results. Details regarding the packing algorithm are described below. 
     In some embodiments, for example, the sensors  216  can include position sensors  224  (e.g., position encoders, potentiometers, etc.) configured to detect positions of structural members (e.g., the robotic arms and/or the end-effectors) and/or corresponding joints of the robotic system  100 . The robotic system  100  can use the position sensors  224  to track locations and/or orientations of the structural members and/or the joints during execution of the task. 
     Discretization Model Processing 
       FIG. 3A  and  FIG. 3B  are illustrations of discretized data used to plan and pack objects in accordance with one or more embodiments of the present technology.  FIG. 3A  illustrates discretized objects and  FIG. 3B  illustrates discretized packing platform for the object packing and planning thereof. For example, the robotic system  100  of  FIG. 1  (via, e.g., the processors  202  of  FIG. 2 ) can map continuous surfaces/edges of real-world objects (e.g., packages, pallets, and/or other objects associated with the task) into discrete counterparts (e.g., unit lengths and/or unit areas). Also, the robotic system  100  can include discretized models/representations of the expected objects stored in the master data  252  of  FIG. 2 . 
     In some embodiments, as illustrated in  FIG. 3A , the robotic system  100  can use discretized object models  302  to plan/derive stacking placements of objects. The discretized object models  302  (shown using dotted lines) can represent exterior physical dimensions, shapes, edges, surfaces, or a combination thereof (shown using solid lines) for known and/or expected objects (e.g., packages, boxes, cases, etc.) according to a discretization unit (e.g., a unit length). In some embodiments, as illustrated in  FIG. 3B , the robotic system  100  can use one or more discretized platform models  304  to plan/derive stacking placements of objects. The discretized platform models  304  can represent a placement surface (e.g., a top surface of the pallet) according to the discretization unit. In some embodiments, the discretization unit can include a length that is preset by a system operator, a system designer, a predetermined input/setting, or a combination thereof. 
     In some embodiments, the discretized platform models  304  can include top views of one or more standard size pallets (e.g., 1.1 m by 1.1 m pallets). Accordingly, the discretized platform models  304  can correspond to pixelated 2D representations of the pallet top surfaces along a horizontal plane (e.g., the x-y plane) according to a grid system utilized by the robotic system  100 . In some embodiments, the discretized object models  302  can include top views (e.g., x-y plane, as illustrated on the left side in  FIG. 3A ) and/or horizontal/profile views (e.g., x-z plane, as illustrated on the right side) for the objects expected/known by the robotic system  100 . Accordingly, the discretized object models  302  can correspond to pixelated 2D/3D representations of the objects. 
     As an illustrative example, the robotic system  100  can use unit pixels  310  (e.g., polygons, such as squares, having one or more dimensions according to the discretization unit) to describe areas/surfaces of targeted objects (via, e.g., the discretized object models  302 ) and loading platforms (via, e.g., the discretized platform models  304 ). Accordingly, the robotic system  100  can pixelate the objects and the loading platforms along the x-y axes. In some embodiments, the size of the unit pixels  310  (e.g., the discretization unit) can change according to dimensions of the objects and/or dimensions of the loading platforms. The size of the unit pixels  310  can also be adjusted (via, e.g., a preset rule/equation and/or operator selection) to balance required resources (e.g., computation times, required memory, etc.) with packing accuracy. For example, when the size decreases, the computation times and the packing accuracy can increase. Accordingly, discretization of the packing tasks (e.g., the target packages and the packing platforms) using adjustable unit pixels  310  provides increased flexibility for palletizing the packages. The robotic system  100  can control a balance between the computation resources/time with the packing accuracy according to unique scenarios, patterns, and/or environments. 
     For the examples illustrated in  FIG. 3A  and  FIG. 3B , the robotic system  100  can expect/process objects corresponding to a first package type  321 , a second package type  322 , a third package type  323 , a fourth package type  324 , and/or a fifth package type  325 . The robotic system  100  can plan and place/stack the packages on a placement pallet  340  that corresponds to the task location  116  of  FIG. 1 . For the placement planning, the robotic system  100  can generate and/or utilize the discretized object models  302  including a first object model  331 , a second object model  332 , a third object model  333 , a fourth object model  334 , and/or a fifth object model  335  that respectively represent the corresponding packages using the unit pixels  310 . Similarly, the robotic system  100  can generate and/or utilize the discretized platform model  304  for the placement pallet  340  using the unit pixels  310 . 
     In some embodiments, the robotic system  100  can round up (e.g., for the discretized object models  302 , such as for the third object model  333  and/or the fourth object model  334 ) the actual dimension of the object such that the unit pixels  310  extend beyond the actual peripheral edges of the object. In some embodiments, the robotic system  100  can round down (e.g., for the discretized platform models  304 ) the actual dimensions of the platform surface such that the unit pixels  310  are overlapped and/or contained within the actual peripheral edges of the object. 
     Based on the discretized data/representations, the robotic system  100  can generate a placement plan  350  for placing/packing the packages onto the placement pallet  340 . The placement plan  350  can include planned locations on the placement pallet  340  for the targeted packages. The robotic system  100  can generate the placement plan  350  for placing one or more of available packages designated for loading/palletization. For example, the robotic system  100  can generate the placement plan  350  for stacking a set of packages from the available packages (e.g., received packages and/or outgoing ordered packages). 
     The robotic system  100  can generate the placement plan  350  according to a set of placement rules, placement conditions, parameters, requirements, etc. In some embodiments, the robotic system  100  can generate the placement plan  350  based on packages grouped according to the set, such as according to the package types (e.g., package types  321 - 325 ), package heights, customer specified priority, fragility (e.g., maximum supported weight, such as for packages stacked thereon), weight range, or a combination thereof. In some embodiments, the robotic system  100  can generate the placement plan  350  according to stacking conditions, such as, e.g., stacking the taller packages further away from the depalletizing unit. Other examples of the placement rules, conditions, parameters, requirements, etc. can include package dimensions, collision free requirement, stack stability, the grouping conditions (e.g., package types, package heights, priority, etc.), package separation requirements or the absence thereof, maximization of total loaded packages, or a combination thereof. Details regarding the placement planning is described below. 
     For the example illustrated in  FIG. 3B , the robotic system  100  can generate the 2D placement plan (e.g., the placement plan  350 ) for a set of packages that correspond to the packages types  321 - 325 . The robotic system  100  can generate the placement plan  350  that places three packages of the first package type  321 , four packages of the second package type  322 , four packages of the third package type  323 , five packages of the fourth package type  324 , and four packages of the fifth package type  325 . The placement plan  350  can group the packages to maximize adjacent groupings of packages with similar height (e.g., equal or within a threshold limit from each other). Accordingly, the robotic system  100  can group the four of the second package type  322  in a 2×2 arrangement located at the lower left-hand corner of the placement pallet  340 . A second grouping of packages (e.g., the packages of the first package type  321 , the fourth package type  324 , and the fifth package type  325 ) can be placed around the initially placed group. Accordingly, the continuous surface area for the first grouping (e.g., at a height of four unit pixels  310 ) and the surface area for the second grouping (e.g., at a height of two unit pixels  310 ) can be maximized. Also, the robotic system  100  can separate the packages of the third package type  323  based on one or more requirements, such as fragility (e.g., limiting the number of supported items) and/or separation requirements. Similarly, the robotic system  100  can generate the 2D placement plan according to boundary requirements (e.g., one or more of the unit pixels  310  from the edge of the placement pallet  340 ). 
     In some embodiments, the robotic system  100  can generate the placement plan  350  based on 2D planning (e.g., x-y footprint, such as a top-view) and/or 3D planning (e.g., x-z or y-z footprint, such as a profile-view). For example, the robotic system  100  can generate the placement plan  350  based on iteratively deriving potential 2D placements along the x-y plane, testing the potential placements according to the placement rules, conditions, etc., calculating a placement score, or a combination thereof. The robotic system  100  can generate the placement plan  350  based on selecting the 2D placement plan that optimizes (e.g., highest or lowest) the placement score. In some embodiments, the robotic system  100  can use the 2D placement plan to further generate a 3D plan (e.g., stacking plan; not shown in  FIG. 3B ). For example, the robotic system  100  can generate the 3D placement plan based on using the 2D placement plan as a layer within a stack. In other words, the robotic system  100  can place the generated 2D placement over/on top of one or more layers (e.g., other 2D placement plans) and/or under/below one or more other layers. 
     As an illustrative example, the robotic system  100  can estimate and consider heights of the placed objects in deriving the 2D plans. For example, the robotic system  100  can pixelate the object heights (e.g., stored in the master data) as shown in  FIG. 3D . Also, the robotic system  100  can map the predetermined height data of the placed object to each of the unit pixels occupied by the object. With the heights mapped to each of the pixels, the robotic system  100  derive placement surfaces of the resulting 2D placement plan  350 . The placement surfaces can each correspond to a derived surface/plane that can have, and support objects placed thereon, such as due same or similar heights of objects forming the derived surface. 
     The robotic system  100  can derive placement surfaces based on identifying groupings of unit pixels that have height values that are within a threshold range of each other. In some embodiments, the robotic system  100  can derive the placement surfaces based on identifying a maximum height for the placement plan  350 . Based on the maximum height, the robotic system  100  can identify the unit pixels in the placement plan  350  having heights matching or within a threshold range from the maximum height. The robotic system  100  can derive an outline based on connecting corners and/or extending edges of outermost/perimeter unit pixels with qualifying heights to derive the placement surface. The robotic system  100  can recursively repeat the process for regions outside of the placement areas using lower heights. For the example illustrated in  FIG. 3B , the robotic system  100  can derive a first placement surface  352 , a second placement surface  354 , and a third placement surface  356 . The first placement surface  352  can correspond to the rectangular area shown in the lower left corner of the placement plan  350  with the maximum height of four unit pixels. The second placement surface  354  can correspond to the surrounding area (shown using dashed lines) with height of two unit pixels. The third placement surface  356  can correspond to the separate area on the right side of the placement plan  350  with the height of one unit pixel. Details for the 2D and 3D placement planning are described below. 
       FIG. 3C  is an illustration of a placement planning process in accordance with one or more embodiments of the present technology. The robotic system  100  (via, e.g., the one or more processors  202  of  FIG. 2 ) can derive the placement plan  350  of  FIG. 3B  for a set of available packages  362 . The available packages  362  can correspond to the objects that need to be packed for an egress shipment and/or storage. For example, the available packages  362  can correspond to incoming objects received via an ingress shipment and/or stored objects that have been ordered for an egress shipment. In some embodiments, the robotic system  100  can use a shipping manifest, an order list, etc. to identify the available packages  362  in real-time, such as directly in response to (i.e., within a threshold duration from) receiving the manifest, the list, etc. Accordingly, the robotic system  100  can use the identified available packages  362  to derive the placement plan  350  in real-time. As such, the robotic system  100  can use real-time conditions, availability, and/or demands to derive the placement plan  350  instead of off-line packing simulators that utilize a hypothetical number/set/combination of packages to derive plans that are applied regardless of real-time conditions. In some embodiments, the robotic system  100  can use devices (e.g., one or more of the processors  202 ) located at the location receiving, storing, and/or sending the objects, such as a shipping hub and/or a warehouse. 
     In some embodiments, as discussed in detail below, the robotic system  100  can group and/or sequence the available packages  362 . The robotic system  100  can use the ordered set of the available packages  362  to derive the placement plan  350 . The robotic system  100  can determine and evaluate unique placement locations/combinations for the available packages  362  to derive the placement plan  350 . In other words, the robotic system  100  can determine a set of potential placement combinations  364  and evaluate (e.g., score) them according to a set of predetermined requirements, conditions, weights, costs, subsequent implications, or a combination thereof. Based on the evaluation, the robotic system  100  can select a placement combination to derive the placement plan  350 . 
     In at least one embodiment, the robotic system  100  can derive the placement plan  350  using an algorithm that iteratively evaluates placements of the sequenced packages. As illustrated in  FIG. 3C , for example, the robotic system  100  can begin the derivation by determining an initial placement for the first package in the available packages  362 . Accordingly, the robotic system  100  can overlap the corresponding discretized object model  302  of  FIG. 3A  over the discretized platform model  304  of  FIG. 3B  at an initial location (e.g., a corner, a middle location, and/or another preset location). The robotic system  100  can track remaining packages  372  based on removing the placed package (e.g., the first package) from the available packages  362 . 
     Based on the initial placement, the robotic system  100  can determine a set of possible placements for the second package in the available packages  362 . The robotic system  100  can determine the set of possible placements according to a predetermined rule, pattern, or a combination thereof. For example, the robotic system  100  can determine the placement locations according to a pattern of locations relative to the previously placed package(s) (e.g., relative to the previously placed package(s)). Also, the robotic system  100  can determine the placement locations based on a minimum/maximum separation distance or a lack thereof required between one or more of the packages. Further, the robotic system  100  can determine the placement locations based on rotating the package (i.e., the corresponding discretized object model  302 ) according to a predetermined amount, such as 90 degrees. In some embodiments, the robotic system  100  can limit the placement possibilities according to a predetermined threshold and/or pattern. Further, the robotic system  100  can update the remaining packages  372  accordingly. 
     The robotic system  100  can repeat the above-described process and iteratively process the available packages  362  until a stopping condition is reached. Some examples of the stopping condition can represent that all packages have been placed (i.e., the remaining packages  372  is empty), the placements cannot be improved (e.g., same evaluation score as the previous tier/iteration), no more packages can be placed over the discretized platform model  304 , or a combination thereof. 
     In some embodiments, the robotic system  100  can track the possible placements and the corresponding potential placement combinations  364  using a search tree  374 . A root of the search tree  374  can correspond to the initial placement and each level or tier can include potential placements of the subsequent package in the available packages  362 . The different tiers can be connected to form a branch that corresponds to a unique combination of placements for the set of packages. 
     For potential placements of each package, the robotic system  100  can identify and eliminate (e.g., represented by ‘X’ in  FIG. 3C ) redundant footprints. For example, at each tier of the search tree  374 , the robotic system  100  can compare (e.g., overlay) the resulting footprints of the potential placement locations/combinations. Based on the comparison, the robotic system  100  can eliminate duplicates of the resulting footprints. In some embodiments, the robotic system  100  can further compare transposed, rotated, and/or mirrored versions of the resulting footprints to eliminate related duplicates. For example, the robotic system  100  can rotate one footprint by 90 degrees and/or transpose the footprint across one or more mirroring lines (e.g. a diagonal line extending across opposing corners, a bisecting line(s) extending along x and/or y directions, or a combination thereof) and compare it to other footprints. 
     Also, for potential placements of each package, the robotic system  100  can identify and eliminate placements that violate one or more requirements/constraints. One example of the requirements/constraints can be based on collision probabilities. The robotic system  100  can calculate an approach path for each placement location and a corresponding collision probability according to the pre-existing footprint, one or more dimensions of the packages, a location of the transfer robot, a previous event or history, or a combination thereof. The robotic system  100  can eliminate the placements where the collision probability exceeds a predetermined threshold. Another example of the requirements/constraints can be a supported weight for stacking (i.e., placing directly on/over one or more support packages) the package. For one or more of the packages under the placement location, the robotic system  100  can calculate a support weight (i.e., a combined weight of packages or portions thereof directly over) based on the weight of the placed package. The robotic system  100  can eliminate the placements where the support weight violates (e.g., exceeds or is within a threshold range from) a fragility requirement (e.g., a maximum supportable weight) for one or more of the packages under the placement location. 
     In some embodiments, the robotic system  100  can track and/or evaluate the placement combinations  364  using a priority queue  376  (e.g., a heap structure etc.). The priority queue  376  can order the placement combinations  364  according to a sequence of preferences. The robotic system  100  can evaluate or score each of the placement combinations  364  according to one or more predetermined criteria. The criteria can include one or more costs associated with already placed items and/or one or more heuristic scores associated with how the current placement affects future placements or possibilities. 
     One example of the criteria can include maximization of footprint density. The robotic system  100  can calculate the footprint density for an outer perimeter  382  for a grouping of packages. In some embodiments, the outer perimeter  382  can be determined based on exposed/outer perimeter edges of the grouping of packages. The robotic system  100  can further enclose surrounding/related areas by extending two or more edges and finding an intersect and/or by drawing a line that connects one or more corners of the footprint. The robotic system  100  can calculate the footprint density as a ratio between an actual occupied area  384  (e.g., a number of unit pixels  310  corresponding to the shaded area) and an empty area  386  (e.g., a number of unit pixels  310  corresponding to the enclosed/related areas). The robotic system  100  can be configured to prefer (e.g., by assigning a higher/lower score) to placement plans that minimize the empty area  386 . 
     Stacking Rules 
       FIGS. 4A-4C  are illustrations of stacking rules in accordance with one or more embodiments of the present technology. The robotic system  100  can use the stacking rules to place packages on top of each other, such as for stacking/placing one or more layers of packages above one or more other layer(s) of packages. The robotic system  100  can use the stacking rules for improving stability of the stacked packages and prevent any packages from slipping and/or tipping during movement of the pallet. For illustrative purposes,  FIGS. 4A-4C  show a top package  452  directly above and supported by (e.g., directly contacting) one or more support packages  454 . 
       FIG. 4A  illustrates a horizontal offset rule  402  used to generate 3D placements (e.g., the 3D placement plan  350 ). The horizontal offset rule  402  can include a regulation, a requirement, or a combination thereof for controlling horizontal offsets of vertical edges/surfaces between stacked items. For example, the horizontal offset rule  402  can be based on an overlap requirement  422 , an overhang requirement  424 , or a combination thereof. The overlap requirement  422  can include a minimum amount (e.g., a percentage or a ratio of length, width, and/or surface area) of overlap between the stacked packages. In some embodiments, the overlap requirement  422  can require that a minimum amount of horizontal dimension/surface area of the top package  452  is overlapped with that of the support package  454 . The overhang requirement  424  can include a maximum amount (e.g., a percentage or a ratio of length, width, and/or surface area) of overhang, such as a portion of the top package  452  that horizontally extends past a perimeter edge/surface of the support package  454 . 
     In some embodiments, the horizontal offset rule  402  can be based on weight, dimension, and/or center-of-mass (CoM) locations  412 . For example, the overlap requirement  422  and/or the overhang requirement  424  can be based on the CoM locations  412 , such as for evaluating a distance between the CoM locations  412  of the top package  452  and the support package  454  relative to a distance between the top CoM location and a horizontal edge/surface of the support package  454  and/or an overhang distance (e.g. a measure along a horizontal direction of a portion of the top package  452  extending past peripheral edge(s) of the support package  454 ). In some embodiments, the horizontal offset rule  402  can be based on a CoM offset requirement  426  that requires the CoM locations  412  of the top packages  452  and the support packages  454  to be within a threshold. The threshold can include a predetermined distance, a threshold limit for a ratio between the offset distance between the CoM locations  412  relative to a horizontal dimension, an overhang distance, an overlapped distance, or a combination thereof. 
       FIG. 4B  illustrates a support separation rule  404  used to generate 3D placements (e.g., a stacking plan). The support separation rule  404  can include a regulation, a requirement, or a combination thereof for controlling a horizontal separation distance  414  between the support packages  454 . The horizontal separation distance  414  can correspond to a horizontal distance between peripheral surfaces/edges of adjacent support packages  454 . In some embodiments, the support separation rule  404  can be further based on locations and/or amounts of overlapped surfaces between the top package  452  and the support packages  454 . For example, the support separation rule  404  can require that the horizontal separation distance  414  to be larger than any overhang distances by a predetermined percentage. Also, the support separation rule  404  can require that the horizontal separation distance  414  extends under the CoM location  412  of the top package  452 . 
       FIG. 4C  illustrates a vertical offset rule  406  used to generate 3D placements (e.g., the 3D placement plan  350 ). The vertical offset rule  406  can include a regulation, a requirement, or a combination thereof for controlling a support height difference  416  between vertical locations of the supporting packages  454 . The support height difference  416  can correspond to a vertical distance between top portions of corresponding support packages  454 , such as for portions that would likely contact the top package  452  placed over the corresponding support packages  454 . In some embodiments, the vertical offset rule  406  can require the support height difference  416  to be under a predetermined threshold requirement for stacking one or more packages on top of the supporting packages  454 . In some embodiments, the support separation rule  404  can vary based on the layer height. For example, when the top package  452  (e.g., the supported package) is part of the top-most layer, the limit for the support height difference  416  can be greater than for the lower layers. 
     The robotic system  100  can generate stacking plans (e.g., a 3D combination of multiple 2D placement plans) according to the stacking rules. For example, the robotic system  100  can generate the 2D placement plans (e.g., the placement plan  350  of  FIG. 3B ) according to height requirements (e.g., for keeping the heights of the package groupings within a threshold distance). Subsequently, the robotic system  100  can generate the stacking plans based on vertically overlapping (e.g., stacking) the 2D placement plans. 
     Stacking Sequence 
       FIG. 5A  is an illustration of an example of a stacking plan  502  (e.g., a plan representing a 3D mapping of the available packages and/or the placement plans  350  correspond to layers within the 3D mapping) in accordance with one or more embodiments of the present technology. For illustrative purposes, the stacking plan  502  is illustrated using a first layer  512 , a second layer  514 , and a third layer  516  for a first stack  520  of the packages (e.g., e.g., at least the packages 1-1 to 1-4, 2-1 to 2-2, and 3-1 to 3-3). Each of the first layer  512 , the second layer  514 , and the third layer  516  can be an instance of the placement plan  350 . The first layer  512  can be on the bottom such that the packages (e.g., at least the packages 1-1, 1-2, 1-3, and 1-4) therein directly contact the placement pallet  340 . The packages (e.g., at least the packages 2-1 and 2-2) in the second layer  514  can be directly on (i.e. having direct contact with) and above the first layer  512 . Similarly, the packages (e.g., at least the packages 3-1 and 3-2) of the third layer  516  can be directly on and contact the second layer  514 . 
     As discussed in detail below, the robotic system  100  can plan each of the layers separately while considering vertical parameters (e.g., supported weight, layer height, etc.). In generating the stacking plan  502 , the robotic system  100  can vertically combine and/or sequence the separate layers according to the vertical parameters and/or the stacking rules. In some embodiments, the robotic system  100  can plan the layers according to vertical placement of the packages. For example, the robotic system  100  can generate the first layer  512  as including all packages that directly contact the placement pallet  340 , such as including the bottom two packages in a second stack  522 . Also, the robotic system  100  can plan the package labeled ‘3-3’ as part of the second layer  514 . In some embodiments, the robotic system  100  can re-plan and/or adjust the layers (e.g., the placement plan  350 ) in generating the stacking plan  502 . For example, the robotic system  100  can adjust the layers to facilitate the stacking/placement sequence. As illustrated in  FIG. 5A , the robotic system  100  can adjust the layers such that the second stack  522  is considered a separate stack (i.e., separate from the first, second, and third layers  512 - 516 ). Accordingly, the robotic system  100  can be free to plan and/or stack the packages of the second stack  522  separately/differently from the layers of the first stack  520 . 
     Also, in some embodiments, the robotic system  100  can move larger packages closest to the transfer unit  104  of  FIG. 1  (e.g., the palletizing robot) to a higher layer to facilitate stacking sequence. Assuming that the transfer unit  104  is to the right of the placement pallet  340  illustrated in  FIG. 5A , the ‘3-3’ package can become an obstacle (i.e., due to its height) if it is placed before packages labeled ‘3-1’ and ‘3-2’. Accordingly, the robotic system  100  can adjust the layers such that the ‘3-3’ package is part of a higher layer (e.g., the third layer  516  instead of the second layer  512 ). As a result, when the robotic system  100  places the packages according to the layers, the ‘3-3’ package can be placed after the ‘3-1’ and ‘3-2’ packages. 
     In other alternative embodiments, the robotic system  100  can separately calculate the stacking or placement sequences based on analyzing the stacking plan  502  without being bound to the layers. For discussion purposes,  FIG. 5B  is an illustration of a stacking sequence  530  (e.g., an identification of a placing order for the available packages) that is not bound by stacking of packages according to the layers in accordance with one or more embodiments of the present technology. The stacking sequence  530  can be for placing a stacked package  532  above a supporting package and horizontally between two end packages. The stacking sequence  530  can be such that the package (labeled ‘1’) furthest from the transfer unit  104  (not illustrated in  FIG. 5B , assumed to be located to the right of the placement pallet  340 ) can be placed first and the second package (labeled ‘2’) is placed on the placement pallet  340  afterwards. The robotic system  100  can calculate the stacking sequence  530  such that the stacked package  532  (labeled ‘3’) is placed before (e.g., third) one of the end packages  534  (labeled ‘4’). As described above, the robotic system  100  can calculate the stacking sequence  530  based on adjusting the one of the end packages  534  to belong to a second layer with the stacked package  532  or based on independently calculating the stacking order from the stacking plan  502 . 
     Operational Flow 
       FIG. 6  is a flow diagram for a method  600  of operating the robotic system  100  of  FIG. 1  in accordance with one or more embodiments of the present technology. The method  600  can be for generating 2D/3D packing plans for placing packages (e.g., cases and/or boxes) on to a platform (e.g., a pallet) and/or for placing the packages accordingly. The method  600  can be implemented based on executing the instructions stored on one or more of the storage devices  204  of  FIG. 2  with one or more of the processors  202  of  FIG. 2 . 
     At block  602 , the robotic system  100  can identify a package set (e.g., the available packages  362  of  FIG. 3C ) and a destination (e.g., the task location  116  of  FIG. 1 , such as a pallet and/or a container for receiving the packages). For example, the robotic system  100  can identify the package set to represent the available packages  362  including packages that are available for packing, located at a source, designated for placement, and/or listed in an order/request/manifest. Also, the robotic system  100  identify a size or a dimension of an area (e.g., a top loading surface of the pallet, such as the placement pallet  340  of  FIG. 3 ) of the task location  116  where the packages can be placed. In some embodiments, the robotic system  100  can identify a size, a dimension, a type, or a combination thereof for a pallet. 
     At block  604 , the robotic system  100  can generate and/or access discretized models (e.g., the discretized object models  302  of  FIG. 3A  and/or the discretized platform models  304  of  FIG. 3B ) corresponding to the package set that represent the available packages  362  and/or the task location  116 . In some embodiments, the robotic system  100  can generate (e.g., in real-time, such as after receiving the order and/or prior to beginning the packing operation, or offline) the discretized models based on dividing physical dimensions of the objects and/or the platform area (e.g., the pallet top surface according to the unit pixel  310  of  FIG. 3B ). The unit pixel  310  can be predetermined (by, e.g., a manufacturer, an ordering customer, and/or an operator), such as at 1 millimeters (mm) or 1/16 inches (in) or greater (e.g., at 5 mm or 20 mm). In some embodiments, the unit pixel  310  can be based (e.g., a percentage or a fraction) on a dimension or a size of one or more of the packages and/or the platform. 
     In some embodiments, the robotic system  100  can access the discretized models stored in the storage devices  204  and/or another device (e.g., a storage device, a database, and/or a server of a package supplier accessed via the communication devices  206  of  FIG. 2 ). The robotic system  100  can access the predetermined discretized models that represents the available packages  362  and/or the task location  116 . For example, the robotic system  100  can access the discretized object models  302  corresponding to the available packages  362  by searching the master data  252  of  FIG. 2  (e.g., a predetermined table or a lookup table) for the available packages and their corresponding models. Similarly, the robotic system  100  can access the discretized platform model  304  representing the platform, such as the identified pallet, where the available packages are to be placed. 
     At block  606 , the robotic system  100  can determine package groupings (e.g., subgroupings of the available packages). The robotic system  100  can determine the package groupings based on the available packages  362  for placing them on the identified platform (e.g., the placement pallet  340 ). The robotic system  100  can determine the package groupings according to similarities and/or patterns in one or more characteristics of the available packages  362 . In some embodiments, as illustrated at block  621 , the robotic system  100  can determine the package grouping by grouping the available packages  362  according to grouping conditions/requirements. Some examples of the grouping conditions/requirements can include a package priority (e.g., as specified by one or more customers), a fragility rating (e.g., a maximum weight supportable by the package), a weight, a package dimension (e.g., a package height), a package type, or a combination thereof. In grouping the available packages  362 , the robotic system  100  can search the master data  252  for the various characteristics of the available packages  362  that match the grouping conditions/requirements. 
     At block  608 , the robotic system  100  can calculate a processing order (e.g., a sequence for considering/deriving placement locations) for the available packages  362  and/or the groupings thereof (i.e., the package groupings). In some embodiments, as illustrated at block  622 , the robotic system  100  can calculate the processing order according to one or more sequencing conditions/requirements. For example, the robotic system  100  can prioritize placement planning of the package groupings according to a number of packages within each of the groupings, such as for processing the package groupings with greater number of packages earlier in the placement planning. In some embodiments, the sequencing conditions can overlap with the grouping conditions, such as for the weight ranges, the fragility ratings, etc. For example, the robotic system  100  can prioritize the processing of the heavier and/or the less fragile packages for earlier processing and/or for placement in lower layers. 
     In some embodiments, the robotic system  100  can prioritize the placement planning according to a combined horizontal area. The robotic system  100  can calculate (via, e.g., multiplying corresponding widths and lengths) or access surface areas of top surfaces of the packages in the groupings using information specified in the master data  252 . In calculating the combined horizontal area, the robotic system  100  can add the surface areas of packages having the same type and/or heights within a threshold range. In some embodiments, the robotic system  100  can prioritize the placement planning of groupings that have the larger combined horizontal area for earlier processing and/or for placement in lower layers. 
     For one or more embodiments, the robotic system  100  can load a buffer with identifiers and/or quantities of the available packages  362 . The robotic system  100  can sequence the identifiers in the buffer according to the groupings. Further, the robotic system  100  can sequence the identifiers in the buffer according to the processing order. Accordingly, the sequenced values in the buffer can correspond to the available packages  362  and/or the remaining packages  372  illustrated in  FIG. 3C . 
     As illustrated at block  624 , for example, the robotic system  100  can calculate the processing order for an initial set (e.g., the package set) of the available packages  362  before implementing the corresponding stacking plan  502  of  FIG. 5 , such as before any of the packages in the package set is placed on the platform. In some embodiments, as illustrated at block  626 , the robotic system  100  can calculate the processing order for a remaining set of the available packages  362  after initiating or while implementing the corresponding stacking plan  502 . For example, as illustrated by a feedback loop from block  616 , the robotic system  100  can calculate the processing order for the remaining set (e.g., a portion of the available packages  362  that have not been transferred to the platform and/or remain at a source location) according to one or more triggering conditions. Example triggering conditions can include stacking errors (e.g., lost or fallen packages), collision events, predetermined retriggering timings, or a combination thereof. 
     At block  610 , the robotic system  100  can generate 2D plans (e.g., the placement plans  350  of  FIG. 3B ) for placing the available packages  362  along a horizontal plane. For example, the robotic system  100  can generate the placement plans  350  to represent the 2D mappings of the available packages  362  along the horizontal plane. The robotic system  100  can generate two or more placement plans based on the discretized models. For example, the robotic system  100  can generate the placement plans  350  based on comparing the discretized object models  302  to the discretized platform model  304 . The robotic system  100  can determine different placements/arrangements of the discretized object models  302 , overlap/compare them to the discretized platform model  304 , and validate/retain the arrangements that are within the boundaries of the discretized platform model  304  when overlapped. The robotic system  100  can designate the packages that cannot be placed within the boundaries of the discretized platform model  304  for another layer (e.g., another instance of the placement plans  350 ). Accordingly, the robotic system  100  can iteratively derive placement locations for the placement plans  350  that represent 2D layers of the stacking plan  502  until each of the packages in the package set have been assigned a location in the placement plans  350 . 
     In some embodiments, the robotic system  100  can generate the placement plans  350  based on the package groupings. For example, the robotic system  100  can determine the arrangements for the packages within one package grouping before considering placements of packages in another grouping. When packages within a package grouping over flows a layer (i.e., cannot fit in one layer or one instance of the discretized platform model  304 ) and/or after placing all packages of one grouping, the robotic system  100  can assign locations for the packages in the next grouping to any remaining/unoccupied areas in the discretized platform model  304 . The robotic system  100  can iteratively repeat the assignments until none of the unassigned packages can fit over remaining spaces of the discretized platform model  304 . 
     Similarly, the robotic system  100  can generate the placement plans  350  based on the processing order (e.g., based on the package groupings according to the processing order). For example, the robotic system  100  can determine a test arrangement based on assigning packages and/or groupings according to the processing order. The robotic system  100  can assign the earliest sequenced package/grouping an initial placement for the test arrangement, and then test/assign the subsequent packages/groupings according to the processing order. In some embodiments, the robotic system  100  can retain the processing order for the packages/groupings across layers (e.g., across instances of the placement plans  350 ). In some embodiments, the robotic system  100  can recalculate and update (illustrated using dashed feedback line in  FIG. 6 ) the processing order after each layer is filled. 
     In some embodiments, as an illustrative example of the above described processes, the robotic system  100  can generate the 2D plans by identifying the different package types (e.g., the first, second, third, fourth, and/or the fifth package type  321 - 325  of  FIG. 3A , respectively) within the package set. In other words, at block  632 , the robotic system  100  can identify unique packages (e.g., as represented by the package types) within each of the package grouping and/or the package set. 
     At block  634 , the robotic system  100  can derive (e.g., iteratively) placement locations for each of the available packages  362 . At block  636 , the robotic system  100  can determine an initial placement location for the unique package first in sequence according to the processing order. The robotic system  100  can determine the initial placement location according to a predetermined pattern as described above. In some embodiments, the robotic system  100  can calculate initial placements for each unique package. The resulting initial placements can each be developed into a unique placement combination (e.g., an instance of the search tree  374  of  FIG. 3C ), such as by tracking the placement plan  350  across iterations. At block  638 , the robotic system  100  can derive and track candidate placement locations for the subsequent packages according to the processing order and/or the remaining packages  372  as described above. Accordingly, the robotic system  100  can iteratively derive the placement combinations  364  of  FIG. 3C . 
     In deriving the placement combinations  364  (e.g., candidate placement locations), the robotic system  100  can test/evaluate locations of the discretized object model  302  of the corresponding package based on iteratively deriving and evaluating candidate stacking scenarios (e.g., potential combinations of unique placement locations for the available packages). The candidate stacking scenarios can each be derived based on identifying unique potential locations (e.g., according to a predetermined sequence/rule for placement locations) for the packages according to the above discussed sequence. The candidate stacking scenarios and/or the unique placement locations can be evaluated according to one or more placement criteria (e.g., requirements, constraints, placement costs, and/or heuristic scores). For example, the placement criteria can require that the discretized object models  302  entirely fit within horizontal boundaries of the discretized platform model  304  when placed at the selected location. Also, the placement criteria can require that placement of the discretized object models  302  be within or over a threshold distance relative to the initial placement location (e.g. such as along a horizontal direction) and/or the previous placement location, such as for adjacent placements or separation requirements. Other examples of the placement criteria can include preferences for adjacently placing packages having smallest difference(s) in one or more package dimensions (e.g., height), the fragility ratings, the package weight ranges, or a combination thereof. In some embodiments, the placement criteria can include collision probabilities that can correspond to locations and/or characteristics (e.g., height) of previously assigned packaged in the layer relative to a reference location (e.g., location of the palletizing robot). Accordingly, the robotic system  100  can generate multiple unique placement combinations (i.e., candidate placement plans for each layer and/or the candidate stacking scenarios that each layer includes multiple layers) of package placement locations. In some embodiments, the robotic system  100  can track the placements of the combination based on generating and updating the search tree  374  across the placement iterations. 
     At block  640 , the robotic system  100  can calculate/update a placement score for each combination/package placement. The robotic system  100  can calculate the placement score according to one or more of the placement conditions/preferences (e.g., package dimensions, collision probabilities, fragility ratings, package weight ranges, separation requirements, package quantity conditions). For example, the robotic system  100  can use preference factors (e.g., multiplier weights) and/or equations to describe a preference for: separation distances between packages, differences in package dimensions/fragility ratings/package weights for adjacent packages, the collision probabilities, continuous/adjacent surfaces at the same height, a statistical result thereof (e.g., average, maximum, minimum, standard deviation, etc.), or a combination thereof. Each combination can be scored according to the preference factors and/or the equations that may be predefined by a system manufacturer, an order, and/or a system operator. In some embodiments, the robotic system  100  can calculate the placement score at the end of the overall placement iterations. 
     In some embodiments, the robotic system  100  can update the sequence of the placement combinations  364  in the priority queue  376  of  FIG. 3C  after each placement iteration. The robotic system  100  can update the sequence based on the placement score. 
     The robotic system  100  can stop the placement iterations, such as when one candidate placement plan is finished, based on determining an empty source status, a full layer status, or an unchanged score status. The empty source status can represent that all of the available packages have been placed. The full layer status can represent that no other package can be placed in the remaining areas of the considered discretized platform model  304 . The unchanged score status can represent that the placement score for the combination remains constant across one or more consecutive placement iterations. In some embodiments, the robotic system  100  can repeat the placement iterations using different initial placement locations and/or different processing order (e.g., for reordering groups having same sequencing value/score associated with the sequencing conditions) to derive other instances of the candidate stacking scenarios. In other words, the robotic system  100  can generate multiple 2D placement plans, where each 2D placement plan can represent a layer within a 3D stack (e.g., an instance of the candidate stacking scenarios). In other embodiments, the robotic system  100  can iteratively consider the 3D effect as a 2D placement plan is derived and begin deriving the next layer as a next iteration when the 2D placement plan becomes full. 
     At block  612 , the robotic system  100  can generate a stacking plan (e.g., the stacking plan  502 ). In some embodiments, the robotic system  100  can begin generating the stacking plan  502  when the placement location of the processed package overlaps one or more previously placed/processed packages. 
     In generating the stacking plan  502  and/or assessing the 2D plans, the robotic system  100  can convert each of the placement combinations  364  and/or the placement plans into 3D states as illustrated at block  652 . For example, the robotic system  100  can assign the height values for the packages to the placement combinations  364 . In other words, the robotic system  100  can generate a contour map (an estimate of a depth map) based on the adding the package heights to placement combinations  364 . 
     With the 3D states, the robotic system  100  can evaluate the placement combinations  364  according to one or more stacking rules (e.g., the horizontal offset rule  402  of  FIG. 4A , the support separation rule  404  of  FIG. 4B , and/or the vertical offset rule  406  of  FIG. 4C ). As an illustrative example, when the placed package is stacked on/over one or more previously processed packages, the robotic system  100  can eliminate any of the placement combinations  364  that violate the overlap requirement  422  of  FIG. 2 , the overhang requirement  424  of  FIG. 4A , the vertical offset rule  406 , the CoM offset requirement  426  of  FIG. 4A , or a combination thereof described above. In one or more embodiments, the robotic system  100  can eliminate any of the placement combinations  364  that violate fragility ratings of one or more packages under the processed package, such as by estimating the supported weights at the overlapped packages and comparing them to the corresponding fragility ratings. 
     For the remaining placement combinations  364 , the robotic system  100  can calculate 3D placement scores or update the placement score, such as illustrated at block  654 . The robotic system  100  can use predetermined preferences (e.g., weights and/or equations) associated with placement costs and/or heuristic values for 3D placements. The predetermined 3D preferences can be similar to the 2D preferences, grouping preferences, sequencing conditions, or a combination thereof. For example, the 3D preferences can be configured to calculate collision probabilities based on the 3D state and to calculate scores that favor the placement combinations with lower collision probabilities. Also, the robotic system  100  can calculate the scores based on the remaining packages  372 , sizes of support areas with common height, number of packed items in the 3D state, difference between the heights of the processed packages, or a combination thereof. In some embodiments, the robotic system  100  can update the sequence of the placement combinations  364  in the priority queue  376  according to the scores. 
     After the 3D states have been processed, the robotic system  100  can update the 2D plans by deriving a placement for the next package in the remaining packages  372 , such as at block  610 . The robotic system  100  can repeat the above-described process until a stopping condition, such as when all of the available packages  362  have been processed (i.e., empty value/set for the remaining packages  372 ) and/or when the placement combinations  364  cannot be improved (also referred to as unimproved combinations). Some examples of unimproved combinations can include when the currently processed placement eliminates the last of the placement combinations  364  in the priority queue  376  due to one or more of the violations and/or when the placement score remains constant for the preferred combinations across a threshold number of iterations. 
     When the stopping condition is detected, such as at block  656 , the robotic system  100  can select one of the derived placement combinations  364  according to the placement scores (e.g., the 2D and/or the 3D related scores). Accordingly, the robotic system  100  can designate the selected placement combination as the stacking plan  502  (e.g., a set of the placement plans  350 ). 
     In some embodiments, as an illustrative example, the robotic system  100  can implement the functions of block  610  and  612  differently. For example, at block  610 , the robotic system  100  can generate the 2D plan (e.g., an instance of the placement plan  350 ) for a bottom layer as described above. In doing so, the robotic system  100  can be configured to place heavier preference (e.g., greater parameter weights) for matching package heights, heavier package weights and/or greater supportable weight for the packages in considering the placements and/or the processing order. The robotic system  100  can derive the first 2D plan for the base layer as described above for block  610 . 
     Once the first 2D layer is complete/full as described above, thereby forming the base layer, the robotic system  100  can convert the placement plan into 3D states as described for block  612 / 652 . Using the 3D information, the robotic system  100  can identify one or more planar sections/areas (e.g., the placement surfaces  352 - 356  of  FIG. 3B ) of the base layer as described above. Using the planar sections, the robotic system  100  can iteratively/recursively derive package placements for the next layer above the base layer. The robotic system  100  can consider each of the planar sections as new instances of the discretized platform models  304  and test/evaluate different placements as described above for block  610 . In some embodiments, the robotic system  100  can derive the 2D placements using the placement surfaces but calculate the score across the entirety of the placement pallet  340 . Accordingly, the robotic system  100  can be configured to follow preferences for larger placement areas for subsequent layers without being limited to the preceding placement areas. 
     Once the iterative placement process stops for the second layer, the robotic system  100  can calculate planar sections (e.g., top surfaces having heights within a threshold range) for the derived layer to generate the 2D placements of the remaining packages/groupings for the next above layer. The iterative layering process can continue until the stopping condition has been met as described above. 
     In some embodiments, the robotic system  100  can separately generate 2D plans (e.g., two or more of the placement plans  350 ) at block  612 . The robotic system  100  can generate the stacking plan  502  based on vertically combining (e.g., arranging/overlapping the 2D placement plans along a vertical direction) the 2D plans. 
     At block  614 , the robotic system  100  can calculate a packing sequence (e.g., the stacking sequence  530  of  FIG. 5B ) based on the stacking plan  502 . As an example, the packing sequence can be for identification of the placing order of the available packages  362 . In some embodiments, as illustrated at block  662 , the robotic system  100  can calculate the packing sequence layer-by-layer. In other words, the robotic system  100  can calculate the packing sequence for each layer and then connect the sequences according to the order/position of the layers from bottom to top. In calculating the packing sequence, in some embodiments, the robotic system  100  can adjust the placement plans as illustrated at block  672 . For example, the robotic system  100  can adjust the placement plans by reassigning one or more of the packages (e.g., packages with heights that increase the collision probabilities for subsequent manipulations/transfers) from a lower-layer placement plan to a higher-layer placement plan. Any packages supported by the reassigned package can also be reassigned to a further higher layer. In other words, the reassigned packages can remain at the same horizontal placement and be associated with a higher layer, such that the packages can be placed later as illustrated in  FIG. 5B . At block  674 , the robotic system  100  can calculate the packing sequence (e.g., the stacking sequence  530 ) based on the adjusted placement plan, such as by packing/manipulating objects that are assigned in the higher layers after the objects assigned in the lower layers. 
     In other embodiments, as illustrated at block  664 , the robotic system  100  can calculate the packing sequence regardless/independent of the layer assignments. In other words, the robotic system  100  can calculate the packing sequence such that packages assigned to a lower layer may be placed after packages assigned to a higher layer. 
     In calculating the packing sequence, both within or across layers, the robotic system  100  can analyze the locations of the packages in the stacking plan  502  according to one or more package dimensions (e.g., heights), relative placement locations, or a combination thereof. For example, the robotic system  100  can sequence placements of boxes further away from a unit/reference location (e.g., location of the palletizing robot) before closer assigned packages. Also, the robotic system  100  can place the taller/heavier packages earlier when their assigned locations are along the perimeters of the placement plan and away from the unit location. 
     At block  616 , the robotic system  100  can implement the stacking plan  502  for placing the available packages  362  on the platform. The robotic system  100  can implement the stacking plan  502  based on communicating one or more motion plans, actuator commands/settings, or a combination thereof to the corresponding device/unit (e.g., the transfer unit  104  of  FIG. 1 , the actuation devices  212  of  FIG. 2 , the sensors  216  of  FIG. 2 , etc.) according to the stacking plan  502 . The robotic system  100  can further implement the stacking plan  502  based on executing the communicated information at the devices/units to transfer the available packages  362  from a source location to the destination platform. Accordingly, the robotic system  100  can place the available packages  362  according to the 3D mapping, where one or more of the available packages  362  are placed/stacked on top of other packages, such as placing the available packages  362  layer-by-layer. Further, the robotic system  100  can manipulate/transfer the packages according to the packing sequence. As such, the robotic system  100  can place the packages layer-by-layer or without such restrictions as described above. 
     Discretization of the tasks and the 2D/3D layering described above provides improved efficiency, speed, and accuracy for packing objects. Accordingly, the reduction in operator inputs and the increase in accuracy can further decrease human labor for the automated packing process. In some environments, the robotic system  100  as described above can eliminate the necessity of sequencing buffers, which can cost around or over $1 million US. 
     CONCLUSION 
     The above Detailed Description of examples of the disclosed technology is not intended to be exhaustive or to limit the disclosed technology to the precise form disclosed above. While specific examples for the disclosed technology are described above for illustrative purposes, various equivalent modifications are possible within the scope of the disclosed technology, as those skilled in the relevant art will recognize. For example, while processes or blocks are presented in a given order, alternative implementations may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and/or modified to provide alternative or sub-combinations. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed or implemented in parallel, or may be performed at different times. Further, any specific numbers noted herein are only examples; alternative implementations may employ differing values or ranges. 
     These and other changes can be made to the disclosed technology in light of the above Detailed Description. While the Detailed Description describes certain examples of the disclosed technology as well as the best mode contemplated, the disclosed technology can be practiced in many ways, no matter how detailed the above description appears in text. Details of the system may vary considerably in its specific implementation, while still being encompassed by the technology disclosed herein. As noted above, particular terminology used when describing certain features or aspects of the disclosed technology should not be taken to imply that the terminology is being redefined herein to be restricted to any specific characteristics, features, or aspects of the disclosed technology with which that terminology is associated. Accordingly, the invention is not limited, except as by the appended claims. In general, the terms used in the following claims should not be construed to limit the disclosed technology to the specific examples disclosed in the specification, unless the above Detailed Description section explicitly defines such terms. 
     Although certain aspects of the invention are presented below in certain claim forms, the applicant contemplates the various aspects of the invention in any number of claim forms. Accordingly, the applicant reserves the right to pursue additional claims after filing this application to pursue such additional claim forms, in either this application or in a continuing application.