Estimation of Ground Reaction Forces from Kinematic Data during Locomotion

Ground reaction forces (GRFs) provide fundamental insight into human gait mechanics and are widely used to assess joint loading, limb symmetry, balance control, and motor function. Despite their clinical relevance, the use of GRF remains underutilised in clinical workflows due to the practical limitations of force plate systems. In this work, we present a force-plate-free approach for estimating GRFs using only marker-based motion capture data. This kinematics only method to estimate and decompose GRF makes it well suited for widespread clinical depolyment. By using kinematics from sixteen body segments, we estimate the centre of mass (CoM) and compute GRFs, which are subsequently decomposed into individual components through a minimization-based approach. Through this framework, we can identify gait stance phases and provide access to clinically meaningful kinetic measures without a dedicated force plate system. Experimental results demonstrate the viability of CoM and GRF estimation based solely on kinematic data, supporting force-plate-free gait analysis.

💡 Research Summary

The paper presents a force‑plate‑free methodology for estimating ground reaction forces (GRFs) during human locomotion using only marker‑based three‑dimensional motion capture data. Recognizing that GRFs are essential for assessing joint loading, gait symmetry, balance, and motor function, the authors aim to overcome the practical constraints of traditional force plates—high cost, space requirements, and the need for specialized expertise—by leveraging kinematic information alone.

A sixteen‑segment rigid‑body model of the whole body (head‑neck, thorax, abdomen, pelvis, bilateral upper arms, forearms, hands, thighs, shanks, and feet) is adopted, based on the Dumas et al. (2011) anthropometric dataset. Segment masses and local centers of mass (CoM) are calculated from gender‑specific regression equations; the hand segment, often missing markers, is reconstructed using Winter’s proportional method (hand length = 0.74 × forearm length). Local coordinate systems follow a modified International Society of Biomechanics (ISB) convention, aligning X with the anteroposterior direction, Y with mediolateral, and Z with vertical.

The whole‑body CoM trajectory is obtained at each frame by mass‑weighted averaging of the sixteen segment CoMs. This trajectory is differentiated twice to yield CoM acceleration; after subtracting gravity, Newton’s second law (Σ R = m a) provides the total external force acting on the body. In single‑stance phases, one leg’s GRF is zero, allowing direct computation of the other leg’s force. In double‑stance phases, the system is underdetermined (two unknown leg forces, one equation). The authors resolve this ambiguity by imposing a “minimum torque‑change” principle: they formulate a quadratic minimization problem that seeks the pair of leg forces producing the smallest change in net torque about the CoM. Solving the resulting Lagrange‑multiplier equations yields closed‑form expressions for the vertical, anterior‑posterior, and mediolateral GRF components for each foot.

Experimental validation used a 10‑meter walk test from a previously collected Asian‑centric activity dataset. Four healthy participants (ages 21–74, both sexes) walked over a Qualisys motion‑capture system (200 Hz) while stepping on Kistler force plates (2000 Hz). Heel‑strike and toe‑off events were detected both from the force‑plate signals and from a sacrum‑based kinematic method (Zeni et al., 2008), confirming high temporal agreement.

CoM estimates were compared against the industry‑standard Visual3D software using identical marker inputs. The custom model showed strong temporal agreement: root‑mean‑square errors (RMSE) of 0.31–0.52 cm in the mediolateral (Y) direction, 3.9–6.2 cm in the anteroposterior (X) direction, and a systematic vertical (Z) offset of 4.3–8.9 cm. The vertical bias stemmed from differing anthropometric models (Dumas vs. Dempster/Hanavan) and was corrected post‑hoc by subtracting 7.2 cm, after which residual Z‑errors fell within 0.01–2.93 cm. The overall three‑dimensional RMSE across trials averaged 5.09 cm, indicating acceptable accuracy for dynamic tracking.

GRF reconstruction demonstrated waveforms that closely matched the measured force‑plate data. The vertical GRF displayed the characteristic double‑peak pattern, the anterior‑posterior component captured braking and push‑off phases, and mediolateral fluctuations reflected balance control. Event detection based on the reconstructed GRFs aligned with the kinematic heel‑strike/toe‑off timestamps, confirming that the estimated forces are sufficiently reliable for gait phase segmentation.

Limitations include the small, homogeneous sample size, restriction to straight‑line walking, and reliance on proportional hand modeling, which may introduce subject‑specific errors in upper‑body dynamics. The minimum torque‑change criterion, while mathematically convenient, does not necessarily represent physiological control strategies; alternative optimization criteria (minimum energy, minimum muscle effort) remain to be explored. Moreover, validation against force‑plate data was performed only for level walking; applicability to stair negotiation, turning, or uneven terrain is yet to be demonstrated.

In conclusion, the study provides a practical, low‑cost pipeline for extracting clinically relevant kinetic information from standard motion‑capture setups. By accurately estimating CoM trajectories and decomposing GRFs without force plates, the method opens the door to broader clinical and rehabilitation use, enabling objective monitoring of gait symmetry, loading patterns, and balance in settings where traditional force‑plate infrastructure is unavailable. Future work should expand validation across diverse populations, incorporate more complex locomotor tasks, and integrate real‑time feedback for personalized rehabilitation interventions.