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. 2023 Jun;39(3):2151-2169.
doi: 10.1109/tro.2022.3226887. Epub 2023 Jan 13.

Data-Driven Variable Impedance Control of a Powered Knee-Ankle Prosthesis for Adaptive Speed and Incline Walking

T Kevin Best  1 , Cara Gonzalez Welker  1 , Elliott J Rouse  2 , Robert D Gregg  1
Affiliations

Data-Driven Variable Impedance Control of a Powered Knee-Ankle Prosthesis for Adaptive Speed and Incline Walking

T Kevin Best et al. IEEE Trans Robot. 2023 Jun.

Abstract

Most impedance-based walking controllers for powered knee-ankle prostheses use a finite state machine with dozens of user-specific parameters that require manual tuning by technical experts. These parameters are only appropriate near the task (e.g., walking speed and incline) at which they were tuned, necessitating many different parameter sets for variable-task walking. In contrast, this paper presents a data-driven, phase-based controller for variable-task walking that uses continuously-variable impedance control during stance and kinematic control during swing to enable biomimetic locomotion. After generating a data-driven model of variable joint impedance with convex optimization, we implement a novel task-invariant phase variable and real-time estimates of speed and incline to enable autonomous task adaptation. Experiments with above-knee amputee participants (N=2) show that our data-driven controller 1) features highly-linear phase estimates and accurate task estimates, 2) produces biomimetic kinematic and kinetic trends as task varies, leading to low errors relative to able-bodied references, and 3) produces biomimetic joint work and cadence trends as task varies. We show that the presented controller meets and often exceeds the performance of a benchmark finite state machine controller for our two participants, without requiring manual impedance tuning.

Keywords: Impedance Control; Optimization; Prostheses.

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Figures

Fig. 12.
Fig. 12.
The average global thigh angle trajectory θth (positive flexion) for 1 m/s 0 deg able-bodied walking, segmented by the phase variable FSM states. The phase variable is defined by linear mappings of θth during S1, S2 and S4, and by a feedforward phase variable rate during S3 and S5. The feedforward rates for S3 and S5 are given by the average rate of change of the phase estimates during the preceding states, which correspond to periods of constant thigh angular velocity.
Fig. 13.
Fig. 13.
Flow chart depicting the FSM states and transition criteria used in the phase variable calculation. States 1–3 (green) occur during the stance phase and states 4–6 (blue) occur during swing. States where phase is directly calculated based on thigh angle are shown as squares and states with feedforward definitions are shown as circles. State 6 is only necessary for non-steady gait and is typically bypassed during steady walking.
Fig. 14.
Fig. 14.
Phase variable trajectories from 4 overground walking bouts recorded while Participant P1 acclimated to the prosthesis between parallel bars. The phase variable is able to parameterize these non-rhythmic motions, allowing the participant to start and stop the gait cycle at will.
Fig. 15.
Fig. 15.
(a) The structure and transition logic of the benchmark finite state machine controller. Tunable parameters ℓcop* and t2→3 controlled the transitions from S1 to S2 and S2 to S3, while constant ground contact and knee velocity thresholds controlled the other three. States in green occur during stance and blue states during swing. (b) Task transition logic indicating how the impedance parameter sets are selected based on the incline estimate γ^.
Fig. 1.
Fig. 1.
A block diagram of the Hybrid Kinematic Impedance Controller presented in this work. Real-time estimates of gait phase s^ and task χ^ define desired joint impedance parameters K, B, θeq and joint angles θd using data-driven models. Depending on if the user is in stance or swing, the torque commands τ are calculated using either an impedance controller or a position controller, respectively.
Fig. 2.
Fig. 2.
Plots of the calculated impedance parameter functions, stiffness K(sst, γ, ν), damping B(sst, γ, ν), and equilibrium angle θeq(sst, γ, ν), for the knee and ankle, projected onto a speed of ν = 1 m/s. These surfaces show the approximated solution to the original optimization problem (4).
Fig. 3.
Fig. 3.
Plots of (a) the mean able-bodied thigh trajectories reported in [24], where positive angles correspond to hip joint flexion, and (b)-(c) the resulting phase variable trajectories at different inclines. Plot (b) shows the trajectories calculated the previous method described in [49] and Plot (c) shows the trajectories calculated using the new phase variable presented in this work. The new method shows no phase pause near push-off and improved linearity, especially at the point of maximum hip extension.
Fig. 4.
Fig. 4.
Photos of above-knee amputee participants P1 and P2 performing various tasks with the HKIC during the experiments.
Fig. 5.
Fig. 5.
Diagrams indicating the locations of the task space sampled during each trial. Each transparent marker indicates the treadmill’s task feedback, sampled at 2 Hz. Each black dot indicates the task combination commanded to the treadmill for a duration of 45 seconds in (a) and 20 seconds in (b).
Fig. 6.
Fig. 6.
Plots of the inter-participant average kinematic and kinetic trajectories produced by each controller over (a) varying inclines at 1 m/s and (b) varying speeds at level ground for the steady-state trials. Able-bodied trajectories from [24] are also shown for reference. The HKIC produced smooth kinematic variations with incline changes as well as increasing knee flexion and ankle push-off torque with increased speed, resembling the able-bodied trajectories.
Fig. 7.
Fig. 7.
Inter-participant RMSE in the observed kinematics (left) and kinetics (right) relative to able-bodied walking data for both the HKIC and FSMC during the steady-state task trials. The error bars represent ±1 standard deviation over lumped participant strides. The HKIC demonstrated lower mean error than the FSMC in 7 of 8 metrics, with particular improvements at the ankle joint. The high knee kinematic error in swing for the HKIC is the result of intentional early extension to promote user confidence that the prosthesis was ready for weight acceptance.
Fig. 8.
Fig. 8.
Inter-participant average cadence for the steady-state task trials as functions of speed for different ramp inclinations: ramp descent (left), level ground (middle), and ramp ascent (right). Error bars represent ±1 standard deviation over lumped participant strides. Both controllers show similar cadence trends as the able-bodied reference (AB) calculated from [24], with increasing step frequency with increasing speed. Overall, the participants preferred longer strides relative to able-bodied, which may be due to the larger mass of the powered prosthesis.
Fig. 9.
Fig. 9.
The inter-participant average prosthesis work per stride over variable (a) inclines and (b) speeds during the steady-state task trials. Error bars represent ±1 standard deviation over lumped participant strides. An able-bodied reference (AB) calculated from [24] shows that the HKIC demonstrated biomimetic energy injection, particularly through a linear increase in ankle work as incline increased, corresponding to 100.6% of the able-bodied rate. Both controllers showed less energy absorption at the knee during steep declines, suggesting that our participants may have had habitual aversions to early stance knee flexion.
Fig. 10.
Fig. 10.
Plot of the inter-participant average kinematic and kinetic error trajectories in the continuously-varying incline trial, relative to able-bodied data [24]. The knee data is shown in the left column and the ankle in the right. Shaded regions represent ±1 standard deviation over lumped participant strides. Aside from intentional discrepancies in the late-swing knee kinematics (see Appendix Section A2), the HKIC showed low RMSE across the gait cycle throughout varying tasks, suggesting appropriately adapting biomechanics.
Fig. 11.
Fig. 11.
Average phase estimate progression calculated in real-time by the HKIC during the continuously-varying task trials for participants P1 and P2. Shaded regions represent ±1 standard deviation. The linearity and consistency of the trajectories illustrate the phase variable’s ability to adapt to continuous task variations and appropriately parameterize the gait cycle.
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