RUL-Aware RRT*: Degradation-Balanced Motion Planning for Robotic Manipulators

Haibo Li; Zhiguo Zeng; Xu Li

cs.ROOct 1, 2026

RUL-Aware RRT*: Degradation-Balanced Motion Planning for Robotic Manipulators

Authors: Haibo Li, Zhiguo Zeng, Xu Li

Organizations: Laboratoire Génie Industriel, CentraleSupélec, Université Paris-Saclay, France · Chair of Risk and Resilience of Complex Systems, CentraleSupélec, Université Paris-Saclay, France · Key Laboratory of Urban Underground Engineering, Beijing Jiaotong University, China

Abstract

Robotic manipulators operating over long durations often experience uneven joint degradation, which causes the weakest actuator to fail prematurely, leads to unplanned downtime, and results in significant operational losses. Traditional motion-planning algorithms do not account for joint health conditions and therefore tend to exacerbate this imbalance during extended operation. To address this challenge, this study introduces the RUL-aware RRT*, a motion-planning method that incorporates joint remaining useful life information into the planning process and adaptively adjusts joint usage in response to evolving health conditions. The method is evaluated across three representative scenarios, namely the Full Health Scenario (FHS), the Heterogeneous Degradation Scenario (HDS), and the Local Degradation Scenario (LDS). The results show that the RUL-aware RRT* effectively suppresses degradation imbalance, delays the emergence of bottleneck failures, and improves the long-term reliability of the robotic system during extended operation. These findings demonstrate that integrating health feedback into motion planning provides a practical and robust pathway for enhancing the durability and operational resilience of manipulators subject to continuous wear.

Figures & tables

Figure 1: Conventional path planning with RRT* (open-loop framework)

Figure 2: RUL-aware path planning with RRT* (closed-loop framework)

Figure 3: Experimental 6-DOF robotic arm used for validation

Scenario	Initial RUL Configuration	No. of Tasks	Evaluation Objective
Full Health Scenario	[1000, 1000, 1000, 1000, 1000, 1000]	80	Verify whether the planner can maintain balanced joint utilization when all joints start equally healthy, preventing early overuse and achieving synchronized degradation.
Heterogeneous Degradation Scenario	[500, 800, 400, 600, 1000, 700]	80	Evaluate the planner’s ability to redistribute joint-level motion usage under non-uniform initial RULs, ensuring adaptive usage balancing and delayed degradation.
Local Degradation Scenario	[100, 1000, 1000, 1000, 1000, 1000]	Until first failure	Test whether the planner can protect the severely degraded joint, reduce its workload, and extend the system’s first failure time while maintaining task feasibility.

Table 1: Summary of test scenarios for RUL-aware motion planning experiments.

Figure 4: RUL degradation curves for different exponent values $p$ . A smaller $p$ produces slower early degradation and a more gradual lifetime decline, while a larger $p$ leads to accelerated wear near the end of life.

Metric	Symbol	Physical Meaning	Tendency	Applicable Scenario(s)
Total RUL Consumption	$\Delta RUL_{\mathrm{sum}}$	Total lifetime consumed by all joints	Lower is better	Full Health Scenario; Heterogeneous Degradation Scenario
Remaining RUL Sum	$RUL_{\mathrm{sum}}^{(T)}$	Total remaining lifetime after all tasks	Higher is better	Full Health Scenario; Heterogeneous Degradation Scenario
RUL Degradation Balance	$CV_{\mathrm{RUL}}^{(T)}$	Uniformity of degradation among joints	Lower is better	Full Health Scenario; Heterogeneous Degradation Scenario
System Lifetime Bottleneck	$RUL_{\min}^{(T)}$	Remaining lifetime of the weakest joint	Higher is better	Full Health Scenario; Heterogeneous Degradation Scenario
System Lifetime Recovery Ratio	$G_{\mathrm{rec}}$	Improvement of bottleneck lifetime vs. baseline	Higher is better	Full Health Scenario; Heterogeneous Degradation Scenario
First Failure Task Index	$k_{\mathrm{fail}}$	Number of tasks before the first joint failure	Higher is better	Local Degradation Scenario

Table 2: Summary of evaluation metrics and their applicability across different test scenarios. Applicable scenarios correspond to those defined in Section 4.2 : Full Health Scenario , Local Degradation Scenario , and Heterogeneous Degradation Scenario .

Figure 5: Comparison of the final remaining useful life (RUL) of six motors under two system conditions: (a–c) Full Health Scenario (FHS) and (d–f) Heterogeneous Degradation Scenario (HDS), for three parameter settings ( $p=0.8$ , $1$ , and $1.5$ ). Each subplot compares the Baseline RRT* and RUL-aware RRT* results for the same configuration. Gray and blue bars represent the mean RUL values of the Baseline RRT* and RUL-aware RRT* planners, respectively, with error bars indicating the standard deviation across runs. The black and blue lines connect the mean RUL values of the Baseline and RUL-aware planners, respectively, while the gray dashed horizontal lines denote the initial reference RUL for each motor.

Figure 6: Evolution of the remaining useful life (RUL) of six motors under the Full Health Scenario (FHS) condition across three parameter settings ( $p=0.8$ , $1$ , and $1.5$ ). Subfigures (a–c) show the baseline RRT* results, while (d–f) present the RUL-aware RRT* outcomes under the same task sequences. The shaded regions represent the standard deviation across multiple experimental runs. Compared with the baseline, the RUL-aware planner achieves more balanced RUL trajectories among all motors, indicating more balanced joint-level motion usage and slower degradation trends.

Figure 7: Evolution of the coefficient of variation (CV) of joint remaining useful life (RUL) in the Full Health Scenario (FHS) over task execution. Each curve corresponds to a specific parameter setting ( $p=0.8$ , $1$ , or $1.5$ ), comparing the Baseline RRT* (red tones) and RUL-aware RRT* (blue tones) planners. Shaded areas around each curve indicate the standard deviation across repeated runs.

Figure 8: Remaining joint lifetime at the end of the Full Health Scenario . For each degradation shape parameter ( $p=0.8$ , $1.0$ , and $1.5$ ), the two adjacent bars correspond to the Baseline RRT* and the RUL-aware RRT* planners. Each bar is stacked: the bottom segment represents the sum of the remaining RUL over the six joints, while the top segment shows the corresponding consumed lifetime, with the total bar height normalized to $6000$ . Error bars on the remaining segment indicate the standard deviation across repeated runs.

Figure 9: Evolution of the coefficient of variation (CV) of joint remaining useful life (RUL) in the Heterogeneous Degradation Scenario (HDS) over task execution. Each curve corresponds to a specific parameter setting ( $p=0.8$ , $1$ , or $1.5$ ), comparing the Baseline RRT* (red tones) and RUL-aware RRT* (blue tones) planners. Shaded areas around each curve indicate the standard deviation across repeated runs.

Figure 10: Remaining joint lifetime at the end of the Heterogeneous Degradation Scenario . For each degradation shape parameter ( $p=0.8$ , $1.0$ , and $1.5$ ), the two adjacent bars correspond to the Baseline RRT* and the RUL-aware RRT* planners. Each bar is stacked: the bottom segment represents the sum of the remaining RUL across the six joints, while the top segment shows the consumed portion, with the total bar height normalized to the initial heterogeneous lifetime ( $500+800+400+600+1000+700=4000$ ). Error bars on the remaining segment indicate the standard deviation across repeated runs.

Figure 11: Comparison of the number of completed tasks for the Baseline RRT* and RUL-aware RRT* planners under the Local Degradation Scenario (LDS) . Each group of bars corresponds to a different shape parameter ( $p=0.8$ , $1$ , and $1.5$ ). Gray and blue bars represent the mean task completion counts of the Baseline and RUL-aware planners, respectively, with black error bars showing the standard deviation across repeated runs. Numeric values above the bars indicate the mean values.

Figure 12: Evolution of the coefficient of variation (CV) of joint remaining useful life (RUL) in the Local Degradation Scenario (LDS) over task execution. Each curve corresponds to a specific parameter setting ( $p=0.8$ , $1$ , or $1.5$ ), comparing the Baseline RRT* (red tones) and RUL-aware RRT* (blue tones) planners. Shaded areas around each curve indicate the standard deviation across repeated runs.

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