⚡ electrical engineering

Risk-Aware Kinodynamic Motion Planning Under Uncertainty For Safe Navigation on Planetary Environments

This paper presents a two-stage framework for risk-aware kinodynamic motion planning in uncertain planetary environments that combines a sampling-based AO-RRT planner with sequential convex optimization, utilizing Conditional Value-at-Risk (CVaR) to achieve over 97% risk reduction in both simulations and hardware experiments.

Original authors: Sachin Sunil Kelkar, Tanmay Dokania, Yashwanth Kumar Nakka

Published 2026-08-12

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Sachin Sunil Kelkar, Tanmay Dokania, Yashwanth Kumar Nakka

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a robot how to walk through a dense, foggy forest. The robot has a map, but the map isn't perfect; the trees might be slightly taller or shorter than drawn, and the ground might be slippery or full of hidden rocks. If the robot just follows the map blindly, it might trip, fall, or crash into a tree it didn't see coming. This is the heart of a big challenge in robotics: how do you plan a path when you aren't 100% sure what the world looks like or how your robot will react to it? Scientists call this "motion planning under uncertainty." It's not just about finding the shortest route; it's about finding the safest route, one that accounts for the fact that things might go wrong. If a robot is exploring Mars, where a crash could mean the end of a multi-million dollar mission, guessing is not an option. You need a way to calculate risk, not just distance.

This paper tackles that exact problem for robots exploring planetary surfaces, like the dusty, rocky landscapes of Mars or the Moon. The authors, working at the Georgia Institute of Technology, developed a two-step "brain" for a robot that helps it navigate safely even when it's unsure about the terrain or its own movements.

First, the robot uses a method called AO-RRT (Asymptotically Optimal Rapidly Exploring Random Trees). Think of this as a robot that quickly sketches out many possible paths through the forest, like a hiker throwing darts at a map to see where they land. But here's the twist: instead of just picking the shortest path, this robot calculates a "risk score" for every step. It asks, "If I go here, how likely am to hit a rock if the ground is slippery?" It uses a mathematical tool called Conditional Value-at-Risk (CVaR) to focus on the worst-case scenarios. If a path looks good on average but has a tiny chance of a catastrophic crash, this tool flags it as dangerous.

Once the robot has a rough, safe sketch of a path, it moves to the second step: Sequential Convex Programming (SCP). Imagine the first sketch was drawn with a shaky hand; it's safe, but maybe a bit jerky or bumpy. The SCP acts like a smooth, steady hand that refines the drawing. It takes that rough path and polishes it, making the movements smoother and more efficient while keeping the safety guarantees intact. It solves a complex math puzzle to ensure the robot doesn't just look like it can make the turn, but actually can make it without slipping or crashing.

The researchers tested this system in two ways: on a computer simulation and on a real robot called the "Leo rover" in a lab that mimicked a rocky, uncertain environment. The results were striking. When they let the robot plan without worrying about risk, it chose a path that looked efficient but incurred a joint collision risk of 0.94. This high risk score indicated that the robot was almost certain to collide with an obstacle, leading to a likely mission failure. However, when they used their risk-aware method, the robot found a path that reduced that collision risk to just 6 × 10⁻³ (a tiny 0.006 chance). Even more impressively, the risk-aware planning reduced the overall risk by over 97% compared to the risky path, all while keeping the energy cost (control cost) almost the same.

In their real-world hardware tests, the robot successfully tracked these safe paths on granular, sandy terrain, even when its wheels slipped. Despite the uncertainty of the slippery ground, the robot stayed on course with an average error of only 6 cm. The paper shows that by teaching robots to fear the worst-case scenarios just a little bit, we can guide them through the unknown without them crashing, making space exploration much safer and more likely to succeed.

Technical Summary: Risk-Aware Kinodynamic Motion Planning Under Uncertainty for Safe Navigation on Planetary Environments

Problem Statement

Autonomous space exploration requires robotic agents to perform motion planning in environments where interactions are often unknown. Specifically, learning terrain mechanics (e.g., for wheeled robots) introduces uncertainties that can lead to risky motion plans, hazardous operations, or mission failures. Furthermore, uncertainties from perception-based systems exacerbate the challenge of safe navigation. Traditional planners that fail to account for actuation degradation, unmodeled terrain dynamics, and sensor noise risk critical mission failure. While previous works have addressed risk-aware geometric trajectories or used risk-neutral planners with risk-constrained controllers, this paper addresses the need to quantify uncertainty in the learned dynamics model itself to generate a risk-aware initial trajectory.

Methodology

The proposed approach performs cost-optimal kinodynamic motion planning with risk awareness through a two-step framework:

1. Uncertainty Quantification and Modeling

Dynamics Model: The system is modeled as a first-order velocity-controlled robot with unmodeled dynamics residue $d(x, u)$ . This residue is approximated using a Lipschitz-continuous neural network.
Conformal Prediction: To quantify the uncertainty of the neural network's output, conformal prediction is employed. The error between predicted residual dynamics and ground truth (measured via motion capture) is computed to establish a confidence set $M$ at a 95% confidence level for linear and angular acceleration errors.
Risk Field Construction: Proximity to uncertain obstacles is modeled as a risk field. For each obstacle $i$ with a boundary uncertainty scale $\sigma_i$ , a risk score $r_i(x)$ is calculated based on the signed distance $d_i(x)$ . These are fused into a single RiskMap bounded in $[0, 1]$ .
Risk-Inflated SDF: A soft risk penalty is applied by inflating the Signed Distance Field (SDF) of obstacles outward by a Conditional Value-at-Risk (CVaR) margin, creating a "RiskSDF" that serves as the constraint boundary.

2. Two-Step Planning Framework

Step A: Risk-Aware AO-RRT (Initial Trajectory Generation)

An Asymptotically Optimal Rapidly Exploring Random Tree (AO-RRT) algorithm generates a dynamically feasible trajectory.
Closed-Loop Risk Computation: Unlike standard planners, edges in the tree are evaluated by tracking the open-loop reference in a closed loop over a horizon, simulating disturbances from the uncertainty set $M$ .
Cost Function: The edge cost incorporates the CVaR of soft collision-constraint violations across the ensemble of disturbance scenarios. This ensures the initial trajectory accounts for both dynamics and obstacle position uncertainty in a single shot, providing a time-consistent risk measure.

Step B: Sequential Convex Programming (SCP) Refinement

The AO-RRT trajectory serves as an initial solution for SCP.
Optimization: The nonlinear problem is cast as locally convex. The objective function jointly minimizes control effort and CVaR (using the Rockafellar-Uryasev epigraph formulation) alongside penalties for terminal errors, defect slacks, and SDF buffer violations.
Constraints: The problem includes affine constraints for dynamics, state/control bounds, and safety clearances relative to the true SDF. Gradients of the risk map are computed exactly via autodiff (JAX).
Solver: The convex subproblem is solved iteratively using the CLARABEL solver until convergence, guaranteeing the nonlinear dynamics are followed while optimizing for smoothness and risk reduction.

Key Contributions

Uncertainty Quantification: Quantifying uncertainty in learning-based dynamics models using conformal prediction.
Risk-Aware AO-RRT: Formulating AO-RRT with closed-loop risk computation (CVaR) as the cost function to generate an initial trajectory that inherently avoids high-risk regions.
Joint Optimization: Casting the nonlinear motion planning problem as a locally convex optimization that jointly minimizes CVaR and control cost within the homotopy provided by the AO-RRT solution, ensuring dynamic feasibility.

Experimental Results

The approach was validated through simulations and hardware experiments on a Leo rover equipped with a ZED 2i stereo camera and Jetson Orin AGX, navigating granular terrain.

Simulation Comparison:
- Without Risk-Aware Cost: The AO-RRT minimized control cost but planned a trajectory directly between high-risk regions, resulting in a joint collision risk of 0.94. SCP refinement reduced this to 0.29, but the trajectory remained in the high-risk homotopy.
- With Risk-Aware Cost: The AO-RRT generated an initial trajectory in the neighborhood of low-uncertainty obstacles. Subsequent SCP refinement achieved a joint collision risk of $6 \times 10^{-3}$ with a control cost of 18.4 units.
- Risk Reduction: The risk-aware approach demonstrated a reduction in risk of over ~97% compared to the risk-neutral approach across trajectories.
Hardware Performance:
- Despite terrain-induced wheel slip, a contraction-based controller using slip-adjusted feedforward velocities tracked the planned trajectory with an RMS error of 6 cm.
- The system successfully constructed risk maps from point clouds and executed dynamically feasible trajectories in an obstacle-rich environment.

Significance and Claims

The authors claim that this work provides a safer, risk-aware solution for motion planning in planetary and lunar robotics applications, which is critical for mission success. By integrating uncertainty quantification directly into the kinodynamic planning loop, the method significantly reduces the probability of mission-critical failure or hazardous operations caused by unmodeled dynamics and perception uncertainties. The paper emphasizes that while SCP alone can refine trajectories, it cannot escape high-risk homotopies; therefore, the risk-aware initialization provided by the AO-RRT is essential for achieving the reported 97% risk reduction. Specifically, the paper notes that the risk-aware AO-RRT step alone generates an initial trajectory solution with **97% less risk** compared to the risk-neutral approach, whereas SCP refinement after a risk-neutral AO-RRT only reduces the joint collision risk by ~69% (from 0.94 to 0.29) but fails to escape the high-risk region.