Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming (2006.02656v2)

Abstract: We present a motion planning algorithm with probabilistic guarantees for limbed robots with stochastic gripping forces. Planners based on deterministic models with a worst-case uncertainty can be conservative and inflexible to consider the stochastic behavior of the contact, especially when a gripper is installed. Our proposed planner enables the robot to simultaneously plan its pose and contact force trajectories while considering the risk associated with the gripping forces. Our planner is formulated as a nonlinear programming problem with chance constraints, which allows the robot to generate a variety of motions based on different risk bounds. To model the gripping forces as random variables, we employ Gaussian Process regression. We validate our proposed motion planning algorithm on an 11.5 kg six-limbed robot for two-wall climbing. Our results show that our proposed planner generates various trajectories (e.g., avoiding low friction terrain under the low risk bound, choosing an unstable but faster gait under the high risk bound) by changing the probability of risk based on various specifications.

• The paper introduces a risk-bounded nonlinear programming framework that optimizes both pose and force trajectories under stochastic gripping conditions.
• It employs Gaussian Process regression to model gripping forces, enabling probabilistic predictions that inform adaptive motion planning.
• Experimental validation on an 11.5 kg six-limbed robot demonstrates stable and aggressive trajectories tailored to varying risk levels.

Overview of "Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming"

The paper in focus delineates a sophisticated approach to the motion planning of limbed robots operating in environments where gripping forces exhibit inherent stochasticity. The authors propose a motion planning framework tailored for robots equipped with grippers, specifically addressing the variability in contact forces and introducing a risk-aware planning technique using Nonlinear Programming (NLP) and chance constraints.

Key Contributions

1. Risk-Bounded Nonlinear Programming: The central contribution is the formulation of a motion planning problem as risk-bounded NLP. By incorporating chance constraints, the planner optimizes both pose and contact force trajectories, allowing the robot to manage different levels of risk associated with uncertain gripping forces. This approach contrasts with traditional deterministic models that tend to be overly conservative.
2. Gaussian Process Modelling for Gripping Forces: The researchers model the gripping forces as random variables using Gaussian Process (GP) regression. This modeling is critical for capturing the stochastic behavior of the gripping forces, enabling the development of a probabilistic prediction framework that supports the planner in managing uncertainty.
3. Experimental Validation: The paper presents detailed experimental validation involving an 11.5 kg six-limbed robot tasked with climbing between walls. The experiments demonstrate the planner's capability to generate trajectories adapted to different risk levels, notably choosing stable paths in low friction zones and employing more aggressive gaits when higher risk is acceptable.

Methodological Insights

• Friction Cone Constraints: The authors incorporate an enhanced friction cone model that accounts for stochastic gripping forces, utilizing chance constraints to ensure compliance within specified risk bounds. This integration allows for adaptable maneuvering, crucial for robots operating in unpredictable terrains.
• Optimization through Two-Step Planning: A two-step optimization strategy is employed for position-controlled robots. Initially, the planner determines feasible force and pose trajectories, followed by calculating the necessary control inputs. This approach mitigates computational issues related to kinematic constraints and force interactions.

Practical and Theoretical Implications

The formulation and results underscore significant advancements in planning algorithms for limbed robots in unpredictable conditions. The probabilistic nature of the planner offers a flexible framework, allowing robots to adjust their behavior based on the risk tolerance dictated by task-specific requirements. The application of GP for modeling force uncertainties provides a robust mechanism to anticipate and react to environmental changes, enhancing robot resilience in real-world applications.

Future Directions

Further research could delve into integrating broader sources of stochasticity, such as sensor noise and terrain variability, into the motion planning framework. Additionally, expanding the framework to incorporate adaptive learning mechanisms would enhance its generalizability across varied robotic platforms and operational scenarios.

Conclusion

This paper successfully introduces a nuanced, risk-aware motion planning paradigm for limbed robots, particularly those operating with stochastic gripping forces. By leveraging advanced probabilistic methods and optimization strategies, the authors significantly contribute to the field of robotic motion planning, paving the way for more adaptive and resilient robotic systems. Such advancements hold promise for expanding the operational envelope of robots in uncertain and dynamically challenging environments.