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Table 2 The relations of variables \(h^i_\mathrm{ref}\), \(h^j_\mathrm{ref}\), \(h^k_\mathrm{ref}\) and \(h^\mathrm{grp}_\mathrm{ref}\) in Fig. 3

From: “Leg-grope walk”: strategy for walking on fragile irregular slopes as a quadruped robot by force distribution

Number Conditions
a-(1) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)
a-(2) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)
a-(3) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)
a-(4) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)
a-(5) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)
a-(6) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)
a-(7) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)
a-(8) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)
b-(1) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} < 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} < 1\)
b-(2) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} < 1\)
b-(3) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} < 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1\)
b-(4) \(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1\)