The development of robotic manipulators and hands that show dexterity, adaptability, and subtle behavior comparable to human hands is an unsolved research challenge. In this article, we considered the passive dynamics of mechanically complex systems, such as a skeleton hand, as an approach to improving adaptability, dexterity, and richness of behavioral diversity of such robotic manipulators. With the use of state-of-the-art multimaterial three-dimensional printing technologies, it is possible to design and construct complex passive structures, namely, a complex anthropomorphic skeleton hand that shows anisotropic mechanical stiffness. We introduce a concept, termed the “conditional model,” that exploits the anisotropic stiffness of complex soft-rigid hybrid systems. In this approach, the physical configuration, environment conditions, and conditional actuation (applied actuation) resulted in an observable conditional model, allowing joint actuation through passivity-based dynamic interactions. The conditional model approach allowed the physical configuration and actuation to be altered, enabling a single skeleton hand to perform three different phrases of piano music with varying styles and forms and facilitating improved dynamic behaviors and interactions with the piano over those achievable with a rigid end effector.

INTRODUCTION

There is increasing interest in the study of nature to provide biological inspiration for the development of robots with physical and cognitive abilities comparable to biological systems (1, 2). Animals interact in highly complex and varied ways with rapidly evolving, information-rich environments (3). Previous work on biologically inspired robotics has demonstrated that the complexity in animals’ behavior results from reciprocal interactions between the controller (brain), the body, and its interactions with the environment (4, 5). Complex behavior does not result from the controller or brain alone but from complexity distributed across the entire system, including the mechanical body (6).

The mechanical properties and design of systems play a considerable role in the intelligent functioning of animals and machines. This can be observed in passivity-based robot control (7, 8). Passivity can, for example, be used to achieve a pendulum-like swing of legs for locomotion, requiring no explicit active control to achieve stable bipedal walking (9). High-functioning passively controlled robots have achieved a range of different behaviors, such as robotic swimming, flying, and manipulation (10). Smart mechanical design enables systems to show exquisite and complex behaviors that are self-stabilizing and energetically efficient at reduced computational cost (11).

Achieving functional behaviors through passivity is crucial for the survival of biological systems; however, as a design method for robotic systems, passivity is known to intrinsically restrict the range of behaviors (12). Underactuated control provides a compromise and can expand the range of behaviors by introducing a coupling between passive mechanics and limited joint actuation (13, 14). This creates behaviors that are highly environmentally dependent and sensitive to changes but limits behavioral diversity, typically with a one-to-one mapping between environment and behavior imposed (15, 16). This limitation can be particularly seen in robotic manipulation and hand design, where passive control and underactuated mechanical design allow only a single (17–19) or, at best, a limited number of behaviors to be achieved (20–24). To leverage the intelligence of passive mechanical bodies, a method for generating a range of behaviors in variable environments is required.

Achieving behavioral diversity in robotics, while using passive dynamics, remains a fundamental challenge. There have been several recent approaches that used passivity to achieve complex (i.e., varied and adaptive) dynamic behaviors, where the complex behavior emerged from many hard-to-control independent mechanical components. One approach was to actively control the mechanical dynamics of the robots by implementing variable stiffness mechanisms that allowed adaptation of the passive behaviors to varying environments (25–27). Although this approach allowed different behaviors to be achieved, the inclusion of actuators limited the scalability and required more complex control (28–31). A second approach was the use of materials to alter or adapt the behavior (32). Soft deformable materials were integrated into robots to expand the diversity of achievable behavioral patterns (33, 34). Behaviors of robots using soft deformable materials were generated through the mechanical dynamics of interactions between the environment and materials (35). The increased compliance of the soft materials provided more flexibility, enabling a wider variety of mechanical dynamics. However, the inherent flexibility of soft materials can result in behaviors that are ill defined and highly variable. A key challenge, therefore, is controlling the mechanical compliance when using softer materials (36, 37). This has been demonstrated with soft robots by using variable stiffness materials to achieve a range of movements and to modulate interactions with the environment (38–40). The synergy between soft bodies and actuation methods could then be used. This allows the movement of soft bodies to be limited or constrained, in turn limiting the requirement for complex additional actuation sources. In particular, work on adaptive synergies (41–43) and tendon routing (44) shows notable breakthroughs and developments with respect to robotic manipulators. Although many of these approaches provide methods for exploiting mechanical passive dynamics, they do not provide a framework for significantly scaling complexity and diversity in behavior.

This paper proposes an alternative approach, using hybrid soft-rigid mechanical structures, where the stiffness of the structures can be set heterogeneously across the body. This builds on well-understood techniques, such as flexure joints, that use anisotropy (25, 45, 46). By taking advantage of state-of-the-art multimaterial three-dimensional (3D) printing techniques, we constructed complex hybrid mechanical structures (47–49). Given appropriate environmental and actuation conditions, this heterogeneity of stiffness could be exploited, with the conditions restricting the joint space such that the observed model of the structure, termed “conditional model,” varies (Fig. 1). In addition to the conditional actuation applied to the system, there is a second observable actuation, the joint actuation, that determines the passivity-based dynamic interactions of the system. The passive interactions arising from the joint actuation may lead to a change in the physical configuration of the structure altering the conditional model (Fig. 1B). This approach provides a conceptual understanding of how complex behaviors can emerge from a passive-based hybrid structure while also informing the design and control necessary to achieve different conditional models and accompanying behaviors.

Fig. 1 Representation of the conditional model. M indicates a motor that provides actuation, and T indicates the resultant torque. (A) A conditional model occurs when a conditional actuation is applied to a physical configuration (e.g., geometry and materials). This model represents the interaction between the system and the environment. There is a secondary internal actuation of the system, the joint interaction, which is dependent on the restriction of the joint space of the conditional model. This results in the passive-based output behavior, leading to a change in the initial physical configuration of the system. (B) For each resultant conditional model, the joint actuation is dependent on different physical configurations from which a second conditional model can be achieved. In this way, it is possible to achieve conditional models that then allow other conditional models to emerge.

The ability to show many conditional models enables diverse and complex mechanical dynamics from a single system. This ability mirrors how the human hand can show highly varied dynamics; for example, a strong fist can be formed to hit a rigid wall, or a soft finger can be used to touch a smooth surface. The range of conditional models that can arise from one passive structure is dependent on the mechanical design, actuation, and environmental conditions. Certain conditional models can only be achieved by first triggering previous conditional models and associated output behaviors; hence, a typical one-to-one mapping of control inputs and behavior can no longer be used (Fig. 1B).

This article investigates the behaviors achievable through the emergence of conditional models. The mechanical complexity of structures, in this case the many interacting mechanical parts with varying stiffnesses, plays a crucial role in the emergence of conditional models. The complexity enables adaptive environmental interactions yet also allows the emergence of specific conditional models and behaviors. The greater the variety of mechanical dynamics within the body of a robot, the wider the variety of conditional models that can be determined through different physical configurations and actuation conditions. Mechanical behavior is bounded by the physical design and geometry of the system, for example, the joint design and the material properties, whereas the environment and surroundings impose conditions on the complex mechanical system contributing to the behavior (41, 50, 51). This approach to designing and controlling a mechanical body leads to richer behavioral diversity in comparison with the previously discussed passivity-based and soft robotic approaches. The diversity of behavior originates from the complexity of the mechanical design while simultaneously reducing the complexity of the required control. To demonstrate this concept, we considered a 3D-printed anthropomorphic robotic hand interacting with a complex environment. Existing anthropomorphic hands often require complex actuation or oversimplify the model such that complex joint behaviors are lost (52–55). In this work, we introduce an approach to producing a near-exact replication of human bone and ligaments by 3D printing, with the behavior dominated by passive dynamics.

To validate the proposed approach, we present a case study of the dexterous robotic hand playing a piano. Piano playing emerges through the coupling between the biomechanics and neuromuscular dynamics of the pianist (mechanical impedance of the finger) and the dynamics of the piano itself (56). Piano playing thus relies on the interaction between the environment and the mechanics of the players’ hand. Piano-playing robotics research dates back to the 1980s (57), with many piano-playing robots developed with a focus on both mechanical and algorithm development (58–62). Most of the robots used rigid finger joints with no compliance such that a high accuracy of finger positioning could be achieved. However, the control required to achieve a variety of more nuanced playing styles, ranging from highly precise rapid movements to softer more adaptive playing, has not been explored thoroughly. Successful expressive and varied piano playing within the fixed environmental conditions provided by the piano posed a rigorous test for the conditional model framework and robotics in general and demonstrated the contributions of this concept.