<p>Legged robots often face a trade-off between stability and energy efficiency, as postures that improve stability typically increase energy consumption, particularly in unstructured environments such as disaster response or exploration sites. While additional appendages can introduce a synergy between stability and efficiency, they also increase hardware and control complexity. In this study, we show that the strategic use of intrinsic kinematic redundancy through posture modulation can provide a stability–efficiency synergy. We design a stability-enhanced gait for a redundant quadruped robot that independently modulates body height <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$z_s$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>z</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> and foot orientation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$n_y$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mi>y</mi> </msub> </math></EquationSource> </InlineEquation> under fixed foothold conditions, and experimentally evaluate its energetic performance. As evaluation metrics, we use the minimum normalized energy stability margin (NESM) over a gait cycle to quantify static stability and the cost of transport (CoT) to assess energy efficiency. Under quasi-static, no-slip, slope-walking conditions, experimental results reveal a strong negative correlation between the minimum NESM and CoT (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\rho =-0.86, p<0.001$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>=</mo> <mo>-</mo> <mn>0.86</mn> <mo>,</mo> <mi>p</mi> <mo><</mo> <mn>0.001</mn> </mrow> </math></EquationSource> </InlineEquation>). In particular, configurations with a lower body height and a foot orientation slightly exceeding the slope angle increased the maximum slope from <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$10^\circ $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$20^\circ $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>20</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> (100%) and reduced CoT by up to 27.7%. These results suggest that NESM can serve as a design-level indicator for selecting energy-efficient and stable gaits based on kinematic posture alone, offering a practical guideline for redundant legged robots operating under limited sensing and computational resources.</p>

Quantitative analysis of stability–efficiency relationship in redundant quadruped locomotion

期刊论文
发表日期：

2026年7月18日

查看全文

Jinhyeok Song,
Seunghyun Lim,
Yeongjoon Jeong,
Taehwan Kim,
Dongwon Yun

摘要

Legged robots often face a trade-off between stability and energy efficiency, as postures that improve stability typically increase energy consumption, particularly in unstructured environments such as disaster response or exploration sites. While additional appendages can introduce a synergy between stability and efficiency, they also increase hardware and control complexity. In this study, we show that the strategic use of intrinsic kinematic redundancy through posture modulation can provide a stability–efficiency synergy. We design a stability-enhanced gait for a redundant quadruped robot that independently modulates body height $z_s$ $z_{s}$ and foot orientation $n_y$ $n_{y}$ under fixed foothold conditions, and experimentally evaluate its energetic performance. As evaluation metrics, we use the minimum normalized energy stability margin (NESM) over a gait cycle to quantify static stability and the cost of transport (CoT) to assess energy efficiency. Under quasi-static, no-slip, slope-walking conditions, experimental results reveal a strong negative correlation between the minimum NESM and CoT ( $\rho =-0.86, p<0.001$ $ρ = - 0.86, p < 0.001$ ). In particular, configurations with a lower body height and a foot orientation slightly exceeding the slope angle increased the maximum slope from $10^\circ $ $10^{\circ}$ to $20^\circ $ $20^{\circ}$ (100%) and reduced CoT by up to 27.7%. These results suggest that NESM can serve as a design-level indicator for selecting energy-efficient and stable gaits based on kinematic posture alone, offering a practical guideline for redundant legged robots operating under limited sensing and computational resources.