Coordinating limbs and spine: (Pareto-)optimal locomotion in theory, in vivo, and in robots

Abstract

Among vertebrates, patterns of movement vary considerably, from the lateral spine-based movements of fish and salamanders to the predominantly limb-based movements of mammals. Yet, we know little about why these changes may have occurred in the course of evolution. Lizards form an interesting intermediate group where locomotion appears to be driven by both motion of their limbs and lateral spinal undulation. To understand the evolution and relative advantages of limb versus spine locomotion, we developed an empirically informed mathematical model as well as a robotic model and compared in silico predictions to in-vivo data from running and climbing lizards. Our mathematical model showed that, if limbs were allowed to grow to long lengths, movements of the spine did not enable longer strides, since spinal movements reduced the achievable range of motion of the limbs before collision. Yet, in-vivo data show lateral spine movement is widespread among a diverse group of lizards moving on level ground or climbing up and down surfaces. Our climbing robotic model was able to explain this disparity, showing that increased movement of the spine was energetically favourable, being associated with a reduced cost of transport. Our robot model also revealed that stability, as another performance criterion, decreased with increased spine and limb range of motion—detailing the trade-off between speed and stability. Overall, our robotic model found a Pareto-optimal set of strides—when considering speed, efficiency, and stability—requiring both spine and limb movement, which closely agreed with movement patterns among lizards. Thus we demonstrate how robotic models, in combination with theoretical considerations, can reveal fundamental insights into the evolution of movement strategies among a broad range of taxa.