Animals navigate unpredictable terrains while frequently changing their direction of movement to evade predators, catch prey, and achieve reproductive success (Daley, 2016; Wilson et al., 2018). Existing research has primarily focused on mechanisms under steady and periodic conditions, such as straight-line movement on level terrain, to comprehend the fundamental mechanisms underlying this skillful locomotion (Shik, 1969; Grillner, 1975). Significant progress has been made in understanding these steady locomotion patterns; in recent years, studies on non-steady locomotion, such as turning and recovery from perturbations, have also gained attention (Daley, 2016; Sponberg et al., 2023). However, from the perspective of control mechanisms, our understanding of non-steady locomotion remains limited. Understanding the control mechanisms of non-steady locomotion is expected to enhance biological knowledge and help develop more agile robots.

This study focuses on the high-speed turning motion of quadrupeds–an intriguing example of non-steady movement. Notably, when quadrupeds are running at their highest speeds, they tend to use a stride pattern known as an asymmetrical, four-beat gait called a gallop, where turning direction is strongly correlated with the order of forelimb contact. During a galloping turn, the outer forelimb lands first as the “trailing limb” while the inner forelimb lands later and initiates the leap as the “leading limb” (e.g., in a rightward turn, the left forelimb serves as the trailing limb and the right forelimb acts as the leading limb; Hildebrand, 1977; Figure 1A). Furthermore, when switching turning directions, quadrupeds exhibit a behavioral pattern known as a “lead change” in which the order of limb contact reverses (Back and Clayton, 2013). Gallop can be classified into rotary gallop and transverse gallop, depending on the sequence of footfalls (Biancardi and Minetti, 2012), and different species and speeds determine which type is used. Regardless of the gallop type, it is consistently observed that the inner forelimb takes on the role of the leading limb during turns (Parkin et al., 2006; Williams and Norris, 2007; Ichikawa et al., 2018; Higurashi et al., 2024; Figure 1B).

The behaviors described above have been examined from a biomechanical perspective in several studies. For instance, as part of research on the dynamical characteristics of animals, one study investigated the ground reaction forces in both the vertical and lateral directions of the inner and outer forelimbs of a horse running in a circular trajectory at a canter (also known as a three-beat gallop, which is an asymmetrical gait; Camus et al., 2012). Another study examined galloping horses on an elliptical track, comparing the duty factors of the inner and outer limbs during curved segments (Parkes et al., 2020). (Hildebrand 1987) suggested that using the inner forelimb as the leading limb during turns allows the animal to maintain support while moving closer to the running trajectory. However, there is still little known about the control mechanism underlying these behaviors.

This research aims to elucidate the control mechanisms underlying adaptive behaviors in galloping turns. We hypothesized that a decentralized control mechanism and trunk movement to generate turning motion are essential components for the emergence of the forelimb footfall sequence observed in gallop turning. This is because decentralized control mechanisms–such as central pattern generators (CPGs) and local sensory feedback–are suggested to be essential for generating locomotor patterns in response to change their situations and environments (Iida and Ijspeert, 2016; Ijspeert, 2017). Since the trunk roll inclination and yaw bending are observed in actual animal turning (Eilam, 1994; Egenvall et al., 2023), so we hypothesized footfall sequence in gallop tuning are naturally generated by compound these decentralized control and trunk motion. To adress this issue, we adopt a decentralized control mechanism, previously proposed by our research group (Owaki et al., 2013; Owaki and Ishiguro, 2017). This is a simple and abstract model based on CPG and local sensory feedback, and it can effectively generate speed-dependent gait transitions through physical interactions and descending modulation. We built a robotic platform and implemented a decentralized inter-limb coordination mechanism from a previous study (Owaki et al., 2013), which enabled locomotion in a straight line. We then extended this mechanism to include trunk movements for body flexion and evaluated the resulting effects. Consequently, we report that an inside leading limb in galloping gaits during turning was spontaneously organized in accordance with trunk roll rotation.

The remainder of this paper is structured as follows. Section 2 describes the robotic platform, along with the autonomous distributed control using local feedback and trunk control. Section 3 presents the experimental setup and results. Section 4 discusses the findings and suggests suggestions for future research.

This study investigates the control mechanisms of quadrupeds during galloping turns using a synthetic approach based on mathematical modeling (Gravish and Lauder, 2018). This section describes the mechanical model of a legged robot, which incorporates roll and yaw degrees of freedom in its trunk, and proposes a decentralized control scheme inspired by animal locomotion.

During turning maneuvers, quadrupedal animals are known to exhibit both trunk yaw bending and roll tilting (Egenvall et al., 2023). This study aims to evaluate the relative contribution of each component–trunk roll tilt and yaw bending–to the emergence of characteristic footfall sequence patterns observed during galloping turns by systematically combining them with the proposed model.

The significance of this study lies in demonstrating that physical interactions through the body also play a crucial role in galloping turns observed by quadrupeds. We confirmed that a trunk roll tilt is indispensable for turning, as the robot consistently turned toward the side of the tilt, with its inner forelimb spontaneously becoming the leading limb. In contrast, changes in trunk yaw angle alone did not induce such a emergence of leading limb. This result may be explained by the fact that trunk roll motion generates an asymmetry in limb-ground clearance, causing the inner limb to contact the ground relatively earlier. Therefore, the determination of the leading limb during turning is likely governed primarily by the physical interactions between the limbs and the ground induced by roll angle modulation. This determination of the leading limb by trunk roll inclination is consistent with previous studies showing that physical interactions through the body contribute to interlimb coordination during straight locomotion. The previously proposed interlimb coordination mechanism (Owaki et al., 2013) used for decentralized autonomous control of the forelimbs in this study has demonstrated that physical interactions among the body and ground is essential to reproduce gait transitions in straight locomotion. Considering the shared interlimb coordination mechanism in this and previous studies, our findings suggest that physical interactions are crucial for generating the adaptive coordination patterns observed in animals, both during straight locomotion and turning.

The robot experiments further indicate that trunk roll angle has a stronger influence on interlimb coordination than yaw-axis bending during galloping turns in quadrupeds; this aligns with previous kinematic and anatomical studies of animals. Kinematic studies on horses moving along small circular paths at a walk, trot, or canter have reported minimal variation in lateral bending angles of the cervicothoracic and thoracolumbar regions, while trunk inclination increases with gait speed (Egenvall et al., 2023). Anatomical studies indicate that spinal lateral bending rarely occurs in isolation and is often accompanied by axial rotation. For instance, a study on cats showed that axial rotational stiffness is lower than lateral bending stiffness, suggesting that much of the flexibility in lateral movements depends on rotational motions involving axial rotation (Macpherson and Ye, 1998). Similarly, axial rotation of the thoracic vertebrae has been observed during lateral bending in horses (Townsend et al., 1983). In this study, Townsend further suggested that utilizing spinal axial rotation, rather than independently controlling limb abduction and adduction, may enable more efficient and coordinated lateral swinging of the limbs. Collectively, these findings suggest that during high-speed galloping turns, trunk roll angle likely plays a more dominant role than yaw-axis bending in shaping interlimb coordination.

To better understand the turning mechanism, we need to investigate whether the control mechanism of this study can also be applied to a flexible trunk, since actual quadrupeds have multiple joint degrees of freedom (Denoix, 1999; Townsend et al., 1983; Macpherson and Ye, 1998). In our experiments, the hardware was specifically designed so that trunk yaw and roll could be independently adjusted, allowing us to examine which factor contributes more strongly to the emergence of the inside-leading limb. As a result, tilting the trunk roll angle alone led to the inner forelimb becoming the leading limb. We consider that this result may be explained by trunk roll tilting motion, in contrast to trunk yaw bending motion alone, creating an asymmetry in limb-ground clearance, resulting in the inner limb contacting the ground earlier. If such asymmetries in clearance between the limbs and the ground are maintained in a multi-joint trunk, the mechanism demonstrated in this study could also be applied in actual quadrupeds.

The wheeled hindlimb structure adopted in this study is considered to capture the essential features of forelimb coordination during galloping turns in quadrupeds. Even in cases where quadrupeds use wheelchairs to support their body in place of their immobile hindlimbs due to fractures or paralysis (Chansangsri and Thawesaengskulthai, 2014), asymmetric turning gaits driven solely by the forelimbs have been observed (Walkin' Pets, 8 30). In such cases, the inner forelimb tends to act as the leading limb and the outer forelimb as the trailing limb, similar to healthy quadrupeds (Jaxom Wolf, 8 30). These findings suggest that a robot with a wheeled hind module is adequate for examining forelimb coordination during galloping turns. As the next step, a mechanical update that includes active hindlimb structures is required to explore balance control with the body having a high center of mass and the role of the hindlimbs in different styles of gallop. For instance, while the forelimb footfall patterns are shared between transverse and rotary gallops, the hindlimb patterns differ: in rotary gallop, the inner hindlimb contacts the ground before the outer hindlimb, whereas in transverse gallop, the order is reversed. Future robotic platforms should allow controllable hindlimb contact and lift-off to investigate how these differences affect maneuverability and motor control across species.

Although our findings are based on thorough experiments using a small dog-sized robot, we anticipate that they can be generalized to medium- to large-sized quadrupeds adept at galloping. In our robot experiments, trunk roll modulation produced trunk leaning, resulting in the inner forelimb becoming the leading limb. In real-world animals of various sizes–including dogs, cheetahs, and horses–this strategy of leaning the trunk during turning (Higurashi et al., 2024; Ichikawa et al., 2018; Egenvall et al., 2023) and using the inner forelimb as leading limb (Higurashi et al., 2024; Ichikawa et al., 2018; Parkin et al., 2006; Williams and Norris, 2007) is consistently employed. We capture these similarities of both robot experiments and real quadrupeds, which suggests that leaning-in is key to the emergence of the inner-leading limb. Therefore, we expect that the proposed mechanism can be applied to quadrupeds of various scales, provided they are capable of leaning their bodies during turning (Biewener and Patek, 2018).

To better understand the agile turning of quadrupeds, in future work we need to investigate control mechanisms that allow trunk angles, such as roll and yaw, to flexibly vary as observed in animals. In this study, to simplify the experimental conditions, we controlled the trunk roll and yaw angles of the robot by fixing their target values. However, actual quadrupeds are known to exhibit dynamic oscillations and twisting of the trunk throughout the turning cycle (Byström et al., 2021; Egenvall et al., 2023). Such flexible behavior may be reproduced by incorporating sensory feedback. For example, in our previous study, we realized cheetah-like running that utilized trunk flexion-extension movements through bidirectional sensory feedback control between the limbs and trunk (Fukuhara et al., 2020a). We believe that this approach could also be applied to the control of trunk roll angles, which may enable more agile turning performance.

In this study, the targeted motion was limited to unidirectional turning during a gallop gait. Although the gait eventually converged such that the inner forelimb on the rolled side became the leading limb and the outer forelimb became the trailing limb, this convergence required four strides (Figures 6C, D). However, actual animals moving in a gallop gait along paths that combine different turning directions, such as a figure-eight (Higurashi et al., 2024), exhibit a phenomenon where they switch the leading limb in mid-air within one or two strides depending on the turning direction (Back and Clayton, 2013). Two key factors are essential to achieve instantaneous limb switching during the swing phase, as seen in actual animals: first factor is the ability to acquire and adjust postural information in response to the turning direction, which requires integrating sensory information from higher centers, such as the visual and vestibular systems; second factor is the ascending modulation that transmits information from the legs to the central nervous system, which is considered necessary to accurately grasp the state of the legs, such as which left or right leg is currently landing first, for switching the leading limb in mid-air. As future work, understanding directional changes in biological gallop requires incorporating elements of higher centers and addressing control mechanisms in which ascending and descending modulations interact.