A Task-to-Intelligence Mapping: When is embodied intelligence worth designing?

While there has been much work in the space of embodied intelligence, we as a field have struggled to define what exactly embodied intelligence is and how it should be used. In this paper, we propose that there are multiple types of embodied intelligence, and that these different types of embodied intelligence are suited to different types of tasks. We introduce a method for classifying tasks according to their objective and occurrence, and we describe how existing work in embodied intelligence fits into this framework. We hope that this proposed framework will initiate a discussion to more formally think about the role that embodied intelligence plays and the value that it brings to engineering and robotics.


The Role of Embodied Intelligence
In the last several years, there has been a large growth in the use of the term "embodied intelligence" [1] and, at the same time, a debate over what exactly embodied intelligence is.Research on "physically intelligent," "morphologically intelligent," and "embodied" systems display a large spectrum of autonomy, from systems with behaviors "hard-coded" into the physical structure [2] to systems that respond to environmental stimuli in ways that approximate computational planning strategies [3].The range of definitions have been just as broad, including attempts such as "The behavior of a system is not merely the outcome of some internal control structure... but it is also shaped by the environment in which the system is physically embedded" (Pfeifer, Lungarella, Iida, 2012 [4]) "The exchange of energy and information between a machine and its environment toward some specified set of goals" (Koditschek, 2021 [5]) "Tight coupling between the body and the brain" (Sitti, 2021 [6]) These definitions emphasize to varying degrees the role of the physical.The first definition, for example, describes for the most part a one-way relationship where the body results in certain types of interactions with the physical world, and the role of intelligence is to accommodate and account for those interactions in determining what actions, behaviors, and adaptions occur.In contrast, Sitti's definition implies a two-way relationship where decision-making is shared 1292 (2023) 012003 IOP Publishing doi:10.1088/1757-899X/1292/1/012003 2 between a physical structure and a more abstract computational one.And definitions such as those proposed by Koditschek acknowledge both options, requiring a physical body and a decision maker, but not requiring a specific interaction between them.A common thread, however, is that intelligence constitutes a system's ability to adapt and respond to stimuli in the environment [7].Thus we see that decade ago, notions of including physics, actuator and sensor models, and environment interactions in control algorithms produced powerful systems capable of reactive behavioral adaptation [8].More recently, the explosion of soft robotics, compliant mechanisms, and minimalist design has further demonstrated how a well-designed body can simplify computation and reduce energetic cost [9].Witnessing this broad range of capabilities that we have managed to achieve, as we look forward to the future role the idea of embodied intelligence will play in engineering, the major question before us seems to be not what embodied intelligence is, but rather where these different types of intelligence most shine.

Costs and Rewards for Embodied Intelligence
The problem of designing a system with embodied intelligence is, at its core, a coupled optimization problem balancing the system's physical body and its computational brain.In determining how this balance should be achieved, it is therefore important to consider the tradeoffs between the value and cost to the system.In this sense, we consider the idea of embodied intelligence always in the context of a particular task that the system aims to accomplish.
For any task, higher levels of intelligence bring greater flexibility and the potential for more effective or efficient task performance.The ability to adapt and learn new behaviors to approach a task more effectively, to change bulk structure to fit task constraints, or to adjust sensorimotor capabilities to enhance information flow and processing all provide a system with options to improve compared to a nonadaptive system.At the same time, the computational and physical structure required to implement such capabilities incurs a cost.Junge et al. [10] identify, for example, cost of design (actuators, mass, volume), cost of control complexity (tuning parameters), and cost of manufacturing and assembly as a few design-time factors to balance.Further execution-time factors, such as additional energy required for task performance when the number of actuators is too high or too low, computational cost associated with planning and control, and memory and bandwidth required to execute desired behaviors, must also be considered.These factors must be balanced against each other in the context of the desired task to produce an overall efficient design.
This strategy of prioritized down-selection is evidenced in biological systems under Darwinian evolution, where physical traits that enhance an organism's capability to accomplish tasks within one's life (i.e., Whole-Organism Performance Capacity) would be selected for and passed on to the next generation (note: many forms may satisfy a performance need) [11,12].For example, locomotion that is directly related to an animal's ability to capture food, avoid becoming food, and disperse into new environments is often a large driver in evolutionary pressures in biological systems [13].The outside world that biological systems inhabit is a complex, non-linear space.Systems inhabiting this space exhibit complicating features such as joint redundancies, time delays between external excitation and internal response, and environmental noise [14,15,16].The nervous system alone cannot successfully enact wanted behaviors with all this internal and external complexity [17].Thus, within biological systems, the interactions between the nervous system, the muscular (and within vertebrates skeletal) system, and the environment, we find emerging adaptive (in some literature "embodied intelligence") behavior [15,18].Without embodied intelligence, biological systems could not successfully respond to tasks inherent to their survival, which would increase individual risk and reduce species fitness.
Turning to engineered systems, we are inspired to understand whether similar trends appear in robotics.

Task-Intelligence Framework for Design
We thus propose a taxonomy of tasks and of embodied intelligence, which we hope will provide a starting point for understanding the relationship between the two and inform future engineering design decisions.

Types of Tasks
We propose that tasks can be classified into four different categories along two axes: task objective and task occurrence (Figure 1).
Along the objectives axis, we observe that task specifications are typically cast either as a timedomain (TD) objective or as a frequency-domain (FD) objective.Time-domain objectives are those tasks where the primary aim is to achieve a particular trajectory or a state at a given point in time.For example, most manipulation tasks involving moving an object from one location to another fall into this category.Task specifications involving minimizing time to completion or total path distance would also be of the time-domain type.Frequency-domain objectives are those tasks where the primary aim is to achieve a particular frequency response.For example, cancellation of noise or vibrations would fall into this category.Task specifications involving minimizing energy consumption would also generally be frequency-domain tasks.While in most cases, the complete task specification will include elements from both categories (e.g., minimize time to completion subject to a total energy budget), typically one will dominate.For example, we would call the previous time minimization example a TD task.We also note that periodic trajectories (e.g., repeated pick-and-place tasks), although performed at some frequency, would under these definitions be considered TD tasks unless the frequency of the trajectory was one of the objectives.
Along the occurrence axis, we categorize tasks by how often they are encountered by the system.High occurrence (HO) tasks are encountered repeatedly over the course of the system's life, while low occurrence (LO) tasks are encountered only infrequently.The task occurrence dictates the total cost that completing the task incurs to the system.For the same task on the same system, a higher occurrence will incur a higher task-specific cost since the task must be completed multiple times.

Task-to-Intelligence Mappings
We suggest that each of these axes influences the value that different modes of intelligence bring to the system.
In particular, the task objective informs what design characteristics have the greatest impact on the task performance.TD tasks relate to the system's state or configuration over time and will be most strongly influenced by design geometry and kinematic structure.In contrast, FD tasks relate to the system's dynamical response and will be most strongly influenced by design mechanics.
At the same time, the task occurrence informs to what extent physical changes in the body of the system will influence task performance.Based on the premise that reactive computation is cheap relative to physical change, LO tasks where tasks change infrequently should be addressed primarily through computational planning and control.In contrast, HO tasks occur with great enough frequency that the benefits of execution-time morphological change are worth the additional costs of actuation and control complexity.Note that, as observed by [19], physically-enacted embodied intelligence presents a value only when the task takes sufficient time to significantly reduce the cost of long-term computational control and improve overall efficiency.We assume for all cases that this threshold has been reached and thus HO tasks, while frequently occurring, are not necessarily short in duration.

Types of Embodied Intelligence
Based on this reasoning, we observe in the literature four major types of embodied intelligence, constituting different degrees of computational versus bodily adaptation exhibited by the system and occupying the four quadrants of the task space.These are: • Computational intelligence: Computationally-implemented embodied intelligence resides in a physical body but, for the most part, does not require a particular body response to complete a task.Instead, planning and control occurs at the computational level and accounts for body dynamics.We propose that this strategy is most suited to TD-LO tasks, that is, tasks that must be completed infrequently and primarily consist of the ensuring that the system reaches a particular configuration or follows a particular trajectory.• Design-time intelligence: In design-time intelligence, also sometimes referred to as "physical inteligence" [6], elements of the task objective are designed into the robot body, simplifying control complexity or enabling the system to complete tasks open-loop with no feedback at all.We propose that this strategy is most suited to FD-LO tasks, that is, tasks where the goal is to achieve a particular steady-state behavior, which changes infrequently over the course of the system's lifetime.• Execution-time kinematic intelligence: Execution-time kinematic intelligence implies kinematic change.Self-reconfigurable systems focusing on shape, geometry, and topology fall into this category.We propose that this strategy is most suited to TD-HO tasks, where a number of specific trajectories or configurations must be achieved repeatedly in time.• Execution-time mechanical intelligence: Execution-time mechanical intelligence refers to self-reconfigurable systems with the ability to change their fundamental mechanics, including mass distribution, stiffness, damping, or other properties that affect their dynamical response.We propose that this strategy is most suited to FD-HO tasks, particular cases where the ultimate goal is to reduce energy consumption over a number of repeatedly occurring tasks.
In the remainder of this paper, we consider the individual quadrants of the task grid, providing examples of existing robotic systems that address these tasks using different types of embodied intelligence.We focus primarily on physically-implemented embodied intelligence -that is, on design-time intelligence, execution-time kinematic intelligence, and execution-time mechanical intelligence -since there is already a great deal of work in the space of computationallyimplemented embodied intelligence and refer the interested reader to [20] for more information on this last type.

Type FD-LO: Design-Time Intelligence
The frequency domain, low occurrence quadrant involves studying tasks where a useful frequency response or steady state behavior is required, and the task specification changes only rarely.For example, a change in environment is one of many factors that could entail a shift in task objective.If it happens that the robot is designed with the sole intention to operate without any qualitative variation in movement, with changes in environmental features occurring rarely in its lifetime, then the task domain in consideration would belong to the FD-LO quadrant.One way to think about FD-LO is that these tasks require "specialists."For these tasks, it would be reasonable to optimize the design of the system for a sole task with an associated natural frequency [21], thus producing design-time intelligence.
One common example of this category is soft swimmers.For example, a flexible bionic flipper was optimized in [22] to generate thrust in a periodic paddling motion by changing the flipper flexibility.The authors found that rigid flippers led to unstable motion while flexible flippers, which were designed to be similar in compliance to real sea lion flippers, were much more effective in propelling the underwater vehicle forward.Similarly, for undulatory motion using segment-wise deformation to mimic serpentine motion [23], the natural dynamics of the compliant robot body was harnessed in half of the actuation cycle to generate sinusoidal waves of deformation and simplify computational control.Since segment stiffness and segment coupling stiffness has a large affect on the natural frequency of motion in segmented robots [24], designtime optimization results in large improvements in energy efficiency when the desired frequency is known.
Similar gains have been achieved in other systems.For example, using different material properties to achieve different mechanics in the C-shape leg of a RHex machine changes the robot's gait and its ability to traverse different types of terrain [25].In our own work, we have also demonstrated that programmable stiffness achieved through origami [26] can be used to control energy storage in a hopping [27] or jumping [28] task.These types of metamaterial are shown to be effective power cascading devices [29] and are easy to design and implement, with very high resilience, as long as the intended task and environmental conditions are known.

Type TD-HO: Execution-Time Kinematic Intelligence
The time-domain, high occurrence quadrant involves studying tasks where the robot's shape or mechanism is important over some duration, and the task must be performed very frequently throughout the lifespan of the system.These tasks often require a specific morphological design [30].For example, mobile robots with wheels are efficient when navigating over smooth terrains.However, on uneven surfaces, the cost of locomotion with wheels becomes high (and sometimes infinite, unable to overcome the obstacles at all).This is when having a second set of kinematic type, or mode, will be helpful, such as having legs or morphing wheels.Ideally, one can incorporate all types of kinematic mechanisms into a single robot.However, the cost of this strategy is high due to the volume and mass of the additional actuators, the limited strength of materials, and financial constraints.Thus, embedding a specific morphological change in a robot design is only cost-effective when the corresponding task is high in occurrence.
As one example, we previously built TurboQuad [31], a robot with the ability to switch between legged and wheeled modes with one set of actuators.The energy consumptions of these three modes are evaluated using an index called the "specific resistance", defined as the averaged power consumption per weight over the averaged forward speed [32].Overall, the specific resistance of the robot is significantly lower in the wheeled mode compared to the legged mode under every speed, thus is the recommended mode of operation on even terrain.However, in the wheeled mode, the robot cannot climb stairs and overcome large obstacles, resulting in an infinite cost.Thus when steering the robot from an uneven terrain to an even terrain, TurboQuad's morphology changes from wheeled to legged, demonstrating execution-time kinematic intelligence.
In addition to locomotion, kinematically changing the shape of the system can enhance the robot's workspace, adding other functionality such as transportability, protection, and viable transmission [33].Similar shape changes have been achieved in manipulation, for example, where changing finger geometries results in a system that can transition between different grasps repeatably [34] or perform reliable perching in aerial vehicles [35].We observe multiple methods of implementing shape change, such as (i) dedicated actuators.These types of robot change shape using an additional set of actuator on top of the driving actuator.One example is the Quattroped [36], a leg-wheel transformable robot that changes "limb" morphology with the help of a servo motor.(ii) shared actuators.These types of robot use the same pair of actuators for morphing and the main task.The previously described Turboquad is of this type.(iii) a control sequence.These types of robot use a particular sequence of motions to reconfigure.
Examples include using different controlling jerks for manipulation [34] or momentum in flight [37].(iv) connection and disconnection.These types of robot change topology by disconnecting and reconnecting parts.Examples include self-reconfigurable modular robots [38] and trusses [39].
In each of these examples, shape change enables the robotic system to access regions of the task space inaccessible to any one of their individual morphologies, but increases their flexibility at the cost of additional design or control complexity.

Type FD-HO: Execution-Time Mechanical Intelligence
The frequency-domain, high occurrence quadrant involves studying tasks where a robot's frequency response must change, and such an action must be performed multiple times throughout the lifespan of the robot, often with qualitative changes in behavior.Locomotive gaits (walking, hopping, swimming, flying), as well as vibration damping, lie in the sphere of frequency domain or cyclic actions.For these systems, their stability and efficiency stem from the ability to vary the mechanical properties (such as stiffness, damping, mass, and shape) of their constituent parts according to task requirements [13].In biological systems, this ability is achieved locally through the neural system as control of low-level mechanics [4].In robots, this strategy corresponds to hierarchical control, where whole-body motions are stimulated as oscillations via central pattern generators (CPGs) and environmental adaptation is delegated to lower-level mechanics (bodily) change.
In this space, researchers have produced a wealth of new materials and actuators capable of changing mechanical properties [40,41,42].By taking advantage of stiffness-tuning capabilities enabled by these actuators, robotic systems have demonstrated improved energetic efficiency in swimming [43] and hopping [44].For example, [19] introduces the very interesting concept of a control-morphology space where the authors lay special emphasis on the variability of mechanics (joint stiffness) of their eel-like robot to simplify the control problem, bringing more efficiency to the robots movements or effecting smooth transitions between two qualitatively different oscillatory behaviors.These systems can match the compliance of humans for safe manipulation in prosthetics and rehabilitative therapy [45].We have previously also shown that these mechanics changes can be computed locally within the body itself without the need for a centralized planner [46].Other mechanics changes such as tunable damping or added transmission systems can additionally simplify oscillatory control [47] and aid in disturbance rejection [48].
Along with the great performance benefits witnessed by execution-time mechanics intelligence, this type of embodied intelligence presents perhaps the greatest integration cost out of all the types, since combining heterogeneous components into an integrated functional system requires tight coupling between materials, mechanisms, sensing, computation, and control, both at the local and the global level [49].Compared to the two other types described previously, work in this space is relatively limited, although we expect to see a large growth along with our rapidly increasing technological capabilities.

Conclusion
We have presented here a framework for thinking about embodied intelligence and how the level at which intelligence is designed into an engineered system relates to a desired task.We have proposed that tasks can be categorized into four quadrants and identified for each quadrant a type of intelligence that would suit the task type.Our framework is based on examples found in the literature, but we acknowledge that a full analysis is yet incomplete.The concept of embodied intelligence is a rich area for exploration, and we have already seen many incredible technological advancements.However, in the end, all design is an optimization between the value to the system and the cost of implementation, and thus our ability to characterize the benefits of embodied intelligence have been hampered by the lack of concrete and detailed efforts to analyze the cost and reward structure of these existing works.We believe that for future research, this type of analysis will bring new insights, expose existing gaps, and open new possibilities in the design of coupled brain-body systems.Now is the time that we should step back and think carefully about when and where different types of embodied intelligence shine, in order to inform future steps in our field that can produce real impact.

Figure 1 .
Figure1.Types of embodied intelligence found in the literature, categorized by potential task applications.Tasks are broken down along task objective and task occurrence axes, which affect the value that different modes of intelligence bring to the system.