Energy-recoverable landing strategy for small-scale jumping robots

Navigating rugged terrain poses significant challenges for small-scale terrestrial mobile robots, chiefly due to the disproportionate size of obstacles relative to robot size [1]. Jumping as a biomimetic locomotion strategy enables the robot to overcome obstacles many times its body size, making it an efficient way to traverse through unstructured environments [2], [3]. This capability is akin to that of jumping animals, which leverage elastic elements to amplify actuator power and exhibit a pause-and-leap behavior. These robots accumulate substantial elastic energy prior to a jump, releasing it during push-off to achieve excellent take-off velocity, typically through latching or series-elastic actuator mechanisms [4], [5], [6], [7], [8], [9]. Powerful obstacle-crossing performance makes jumping robots potentially useful in applications such as planetary exploration and post-disaster rescue.

Jumping efficiency, denoted as $\eta$, is a critical performance metric for these robots. It is typically defined as the ratio of translational kinetic energy at take-off to the pre-jump stored energy [10], [11], [12], reflecting the efficiency of elastic energy utilization in take-off and directly influencing locomotion efficiency. Factors affecting $\eta$ mainly include friction losses, premature lift-off, and ineffective kinetic energy conversion. Premature lift-off means that the energy stored in the elastic elements is not fully released at the moment the robot’s leg leaves the ground, which can be improved by modulating the output force characteristics of the jumping mechanism [13], [14], [15]. Ineffective kinetic energy conversion is the partial conversion of elastic energy into kinetic energy unrelated to jump performance, including rotational energy of the body or the leg. This part of energy can be reduced by decreasing the leg inertia or reducing moments exerted on the body during the push-off by optimizing the jumping mechanism design [16], [17], [18].

A full jump cycle includes push-off, projectile motion in mid-air, and landing. In addition to the push-off phase, the robot behavior in other phases also affects the locomotion efficiency. During the mid-air motion, the effect of air resistance or lift on the jumping range is usually negligible for animals or robots weighing more than 10 g, unless they are equipped with the appropriate appendages for generating gliding motion [19]. Integrated jumping-gliding motion can significantly extend the jump distance, thus reducing cost of transport and improving locomotion efficiency [20], [21], [22]. Landing as a mandatory phase for every jumping robot involves a rapid energy transformation. Like jumping insects, most miniature jumping robots collide rigidly with the ground during landing [23], [24], [25]. Passive elastic elements, such as semi-circular hoops, cages, and soft materials, are adopted by some small-scale jumping robots to slow down the energy conversion during landing and reduce impact forces [2], [26], [27], [28]. Legged landings are common in use among medium or large multi-legged robots with many degrees of freedom (DOFs) for active dissipation of collision energy [29], [30], [31], [32]. The small leg stroke and limited onboard sensing and computational capabilities make it particularly challenging for small-scale jumping robots to make legged landings, of which Salto −1P is the only tetherless example to successfully perform the legged landing [33]. However, existing jumping robots remove all the jump energy during landing, regardless of the existing landing method, which results in a large amount of wasted energy. In other words, recovering jump energy for the following jump circle can enhance the locomotion efficiency of the jumping robot, which inspires this work.

In this paper, we propose a landing strategy for the jumping robot to recycle mechanical energy into the springs in the jumping mechanism during landing. A jumping mechanism with controllable characteristics of being mono-stable or bi-stable is used for both jumping and energy recoverable landing. During the jumping phase, the mechanism is transitioned from a bi-stable to a mono-stable state, allowing the leg to extend and the energy stored in the springs to be converted into the robot’s kinetic energy. By controlling the jumping mechanism to an appropriate bi-stable state before the touchdown, the robot can recover some of its mechanical energy into the springs after landing. The energy recovery is ensured by the mechanism’s physical intelligence, requiring only angular position maintenance of the motor during landing. A small-scale 165 g jumping robot prototype with onboard sensing, computation, and energy is developed (Fig. 1), achieving a 94 cm jumping height. Experiments demonstrate successful energy recovery for landing velocity angle from 0° to 30° and recovers at least 52.9% of the jump energy into the springs, suggesting its applicability across different jumping trajectories.

The remainder of this paper is organized as follows. Section 2 presents the landing concept based on the bi-stability of the jumping mechanism. Section 3 develops the touchdown collision model, landing dynamics model, and motor control strategy and gives the design detail of the robot prototype. Section 4 presents the landing simulation results at different conditions. Section 5 gives experimental demonstrations of the legged landings.