Erratum to: Low stiffness design and hysteresis compensation torque control of SEA for active exercise rehabilitation robots

1 Erratum to: Auton Robot DOI 10.1007/s10514-016-9591-z

In the original publication of the article, the following errors were occurred. These errors have been corrected with this erratum.

In Fig. 4, labels of sub-figures (b) and (c) should be changed each other, and x-axis labels ‘Time (sec)’ of lower two figure should be read as ‘Deformation (rad)’. In Fig. 5, $\theta _pre$ should be read as $\theta _{pre}$. In pages 8-9, all subscripts k should be read as i. In page 9, $\theta _{a}, \theta _{b}, \theta _{c}$, and $\theta _{d}$ should be read as $\theta _{A}, \theta _{B}$, $\theta _{C}$, and $\theta _{D}$ , and in Eq. 26, $f_{ac}$ should be read as $f_{dc}$.

In Algorithm 1, the following typos has occurred in line numbers 8, 9, 13, 14, 15, 18 and 20. The corrected Algorithm is given below:

Table 4 Parameters of three springs for the proposed hysteresis model

In Table 4, the $f_{al+}$ was misspelled in the 4th, 5th, 6th, and 7th rows of 1st column. From 4th row, $f_{al+}$ should be read as $f_{ac+}$, $f_{ac-}$, $f_{dc+}$, and $f_{dc-}$. The corrected Table is given below:

In page 13, “The spring block of Fig. 12 has...” should be read as “The spring block in Fig. 12 means physical spring, and the block for the proposed model means the estimation model. The latter block has...”, and “Figure 12 shows the experimental results...” should be read as “Figure 14 shows the experimental results...”. In Fig. 15, the caption should be corrected as “The experiment results of torque control without external motion. a Reference torque trajectory. b Torque error for three cases.”

In Eq (43) of Appendix 1, $s_{-,max}$ should be read as $s_{-,min}$ and in page 19, “where $s_{+,min}$ and $s_{,min}$ are...” should be read as “where $s_{+,min}$ and $s_{-,min}$ are...”.

The Acknowledgement should be corrected following the official format of the government ministry.