Comparative Study on Agility, Efficiency, and Impact Absorption of Bipedal Robots with Active Toes

The spine plays a crucial role in the dynamic locomotion of quadrupedal animals, improving the stability, speed, and efficiency of their gait, especially for fast-paced and highly agile movements. Therefore, the spine is also a promising and natural way to extend the capabilities of quadruped robots. This paper empirically investigates the benefits of an actuated spine for learning agile quadruped locomotion. We evaluate whether the use of the spine brings benefits in terms of high-speed running, climbing stairs, climbing high-angle slopes, hurdling, and crawling scenarios. We conducted an empirical study in MuJoCo simulation using the Silver Badger robot from MAB Robotics with an actuated 1-DOF spine in the sagittal plane. The obtained results show that the use of the spine provides the robot with increased agility and allows it to overcome higher stairs, steeper slopes, higher obstacles, and smaller passages.

Quadruped robots are often designed with rigid feet to simplify control and maintain stable contact during locomotion. While this approach is straightforward, it limits the ability of the legs to absorb impact forces and reuse stored elastic energy, leading to higher energy expenditure during locomotion. To explore whether compliant feet can provide an advantage, we integrate foot compliance into a reinforcement learning (RL) locomotion controller and study its effect on walking efficiency. In simulation, we train eight policies corresponding to eight different spring stiffness values and then cross-evaluate their performance by measuring mechanical energy consumed per meter traveled. In experiments done on a developed quadruped, the energy consumption for the intermediate stiffness spring is lower by ~ 17% when compared to a very stiff or a very flexible spring incorporated in the feet, with similar trends appearing in the simulation results. These results indicate that selecting an appropriate foot compliance can improve locomotion efficiency without destabilizing the robot during motion.

Low-friction surfaces challenge bipedal locomotion by limiting the contact forces available during stepping. Inspired by penguin waddling, we investigate how lateral torso motion and center of mass (COM) placement affect locomotion as surface friction changes. Using a five-actuator biped, we compare an upright-gait strategy with a penguin-inspired torso-over-stance-leg strategy across multiple COM placements in simulation and hardware. In the 3-D simulator MuJoCo, we sweep through sinusoidal leg and hip actuation parameters across four friction coefficients mu = 0.1, 0.3, 0.5, 0.7. In simulation, torso-over-stance-leg motion produces more successful controllers and higher forward speeds at low friction, with the highest speed occurring for the high-COM configuration. Hardware experiments show the same low-friction speed trend: at mu=0.12, torso-over-stance-leg motion increases forward speed and reduces cost of transport at both tested COM ratios, and the higher COM also improves both measures. The high-COM penguin configuration is the fastest and most energy efficient while maintaining low sideways foot motion. At mu=0.45, the COM trend reverses: the lower-COM configurations are faster and more energy efficient, while gait strategy has little effect on forward speed but still changes sideways foot motion. These results show that the effects of lateral torso motion and COM placement depend on the available friction, and that forward speed, energy use, and slip-related foot motion can be modulated with a penguin-inspired torso motion on hardware.