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Here, we study how propulsive and perturbing appendages together contribute to successful strenuous ground self-righting. Some of these animals also use other appendages or the body to propel against the ground ( Brackenbury, 1990 Davis, 1968 Domokos and VГЎrkonyi, 2008 Faisal and Matheson, 2001 Hoffman, 1980 Li et al., 2019), and such vigorous appendage flailing appears to be a desperate, wasteful struggle.

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In particular, vigorous appendage flailing is a ubiquitous behavior observed across a diversity of species ( Ashe, 1970 Brackenbury, 1990 Davis, 1968 Delcomyn, 1987 Domokos and VГЎrkonyi, 2008 Faisal and Matheson, 2001 Full et al., 1995 Hoffman, 1980 Kleitman and Koppanyi, 1926 KoppГЎnyi and Kleitman, 1927 Li et al., 2019 Silvey, 1973 Zill, 1986). Often, rather than using a single type of appendages or just deforming the body without using appendages, animals use them together to propel and perturb the body to destabilize from the upside-down state ( Brackenbury, 1990 Davis, 1968 Domokos and VГЎrkonyi, 2008 Faisal and Matheson, 2001 Hoffman, 1980 Li et al., 2019). A diversity of strategies have been described, including using appendages such as legs, wings, tail, and neck and deforming the body substantially. Ground self-righting has been studied in a diversity of animals, including insects ( Brackenbury, 1990 Delcomyn, 1987 Faisal and Matheson, 2001 Frantsevich and Mokrushov, 1980 Li et al., 2019 Sherman et al., 1977 Zill, 1986), crustaceans ( Davis, 1968 Silvey, 1973), mollusks ( Hoffman, 1980 Weldon and Hoffman, 1979 Zhang et al., 2020), and vertebrates ( Ashe, 1970 Bartholomew and Caswell, 1951 Creery and Bland, 1980 Domokos and VГЎrkonyi, 2008 GoluboviД‡ et al., 2015 KoppГЎnyi and Kleitman, 1927 Malashichev, 2016 Pellis et al., 1991 Robins et al., 1998 Vince, 1986 Winters et al., 1986). Often, animals struggle to self-right quickly and needs multiple attempts ( Brackenbury, 1990 Domokos and VГЎrkonyi, 2008 Full et al., 1995 Hoffman, 1980 KoppГЎnyi and Kleitman, 1927 Li et al., 2019 Silvey, 1973) to self-right due to constraints from morphology, actuation, and the terrain ( Domokos and VГЎrkonyi, 2008 Faisal and Matheson, 2001 GoluboviД‡ et al., 2017 GoluboviД‡ et al., 2013 Li et al., 2019 Steyermark and Spotila, 2001). For example, to self-right, cockroaches must overcome potential energy barriers seven times greater than the mechanical energy required per stride for steady-state, medium speed running (eight body lengths s в€’1) ( Kram et al., 1997) or, exert ground reaction forces eight times greater than that during steady-state medium speed running (five body lengths s в€’1) ( Full et al., 1995). Ground self-righting is a strenuous task. Similarly, ground self-righting is critical for the continuous operation of mobile robots (for a review, see Li et al., 2017).

Thus, it is crucial for animals to be able to self-right at a high probability because it can mean the difference between life and death. The longer an animal is flipped over and stranded, the more susceptible it is to risks like predation, starvation, desiccation ( Steyermark and Spotila, 2001), and limited mating success ( Penn and Jane Brockmann, 1995). Ground self-righting is a critical locomotor capability that animals must have to survive (for a review, see Li et al., 2019). Our work demonstrated the usefulness of potential energy landscape for modeling self-righting transitions. The model also revealed that the stereotyped body motion during self-righting emerged from physical interaction of the body and appendages with the ground. A potential energy landscape model revealed that, although wing opening did not generate sufficient kinetic energy to overcome the high pitch potential energy barrier to somersault, it reduced the barrier for rolling, facilitating the small kinetic energy from leg flailing to probabilistically overcome it to self-right. The robotвЂ™s self-righting probability increased with wing opening and leg flailing amplitudes. We then developed a robot with similar strenuous self-righting behavior and used it as a physical model for systematic experiments. Adding mass to increase hind leg flailing kinetic energy increased the animalвЂ™s self-righting probability. Here, we studied whether wing opening and leg flailing together facilitate strenuous ground self-righting. During winged self-righting, the animal flails its legs vigorously. As it repeatedly attempts this, the animal probabilistically rolls to the side to self-right.

To do so, the discoid cockroach often pushes its wings against the ground to begin a somersault which rarely succeeds. Terrestrial animals must self-right when overturned on the ground, but this locomotor task is strenuous.

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