Safe Dynamic Motion Generation in Configuration Space Using Differentiable Distance Fields

Generating collision-free motions in dynamic environments is a challenging problem for high-dimensional robotics, particularly under real-time constraints. Control Barrier Functions (CBFs), widely utilized in safety-critical control, have shown significant potential for motion generation. However, for high-dimensional robot manipulators, existing QP formulations and CBF-based methods rely on positional information, overlooking higher-order derivatives such as velocities. This limitation may lead to reduced success rates, decreased performance, and inadequate safety constraints. To address this, we construct time-varying CBFs (TVCBFs) that consider velocity conditions for obstacles. Our approach leverages recent developments on distance fields for articulated manipulators, a differentiable representation that enables the mapping of objects' position and velocity into the robot's joint space, offering a comprehensive understanding of the system's interactions. This allows the manipulator to be treated as a point-mass system thus simplifying motion generation tasks. Additionally, we introduce a time-varying control Lyapunov function (TVCLF) to enable whole-body contact motions. Our approach integrates the TVCBF, TVCLF, and manipulator physical constraints within a unified QP framework. We validate our method through simulations and comparisons with state-of-the-art approaches, demonstrating its effectiveness on a 7-axis Franka robot in real-world experiments.

Configuration Space Distance Fields for Manipulation Planning

The signed distance field is a popular implicit shape representation in robotics, providing geometric information about objects and obstacles in a form that can easily be combined with control, optimization and learning techniques. Most often, SDFs are used to represent distances in task space, which corresponds to the familiar notion of distances that we perceive in our 3D world. However, SDFs can mathematically be used in other spaces, including robot configuration spaces. For a robot manipulator, this configuration space typically corresponds to the joint angles for each articulation of the robot. While it is customary in robot planning to express which portions of the configuration space are free from collision with obstacles, it is less common to think of this information as a distance field in the configuration space. In this paper, we demonstrate the potential of considering SDFs in the robot configuration space for optimization, which we call the configuration space distance field. Similarly to the use of SDF in task space, CDF provides an efficient joint angle distance query and direct access to the derivatives. Most approaches split the overall computation with one part in task space followed by one part in configuration space. Instead, CDF allows the implicit structure to be leveraged by control, optimization, and learning problems in a unified manner. In particular, we propose an efficient algorithm to compute and fuse CDFs that can be generalized to arbitrary scenes. A corresponding neural CDF representation using multilayer perceptrons is also presented to obtain a compact and continuous representation while improving computation efficiency. We demonstrate the effectiveness of CDF with planar obstacle avoidance examples and with a 7-axis Franka robot in inverse kinematics and manipulation planning tasks.

GeoPro-VO: Dynamic Obstacle Avoidance with Geometric Projector Based on Velocity Obstacle

Optimization-based approaches are widely employed to generate optimal robot motions while considering various constraints, such as robot dynamics, collision avoidance, and physical limitations. It is crucial to efficiently solve the optimization problems in practice, yet achieving rapid computations remains a great challenge for optimization-based approaches with nonlinear constraints. In this paper, we propose a geometric projector for dynamic obstacle avoidance based on velocity obstacle (GeoPro-VO) by leveraging the projection feature of the velocity cone set represented by VO. Furthermore, with the proposed GeoPro-VO and the augmented Lagrangian spectral projected gradient descent (ALSPG) algorithm, we transform an initial mixed integer nonlinear programming problem (MINLP) in the form of constrained model predictive control (MPC) into a sub-optimization problem and solve it efficiently. Numerical simulations are conducted to validate the fast computing speed of our approach and its capability for reliable dynamic obstacle avoidance.

Whole-body Dynamic Collision Avoidance with Time-varying Control Barrier Functions

Recently, there has been increasing attention in robot research towards the whole-body collision avoidance. In this paper, we propose a safety-critical controller that utilizes time-varying control barrier functions (time varying CBFs) constructed by Robo-centric Euclidean Signed Distance Field (RC-ESDF) to achieve dynamic collision avoidance. The RC-ESDF is constructed in the robot body frame and solely relies on the robot's shape, eliminating the need for real-time updates to save computational resources. Additionally, we design two control Lyapunov functions (CLFs) to ensure that the robot can reach its destination. To enable real-time application, our safety-critical controller which incorporates CLFs and CBFs as constraints is formulated as a quadratic program (QP) optimization problem. We conducted numerical simulations on two different dynamics of an L-shaped robot to verify the effectiveness of our proposed approach.

Fast Path Planning for Autonomous Vehicle Parking with Safety-Guarantee using Hamilton-Jacobi Reachability

We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level bidirectional A* search algorithm. In high-level reachability analysis, a backward reachable tube (BRT) concerning vehicle dynamics is computed by the HJ analysis and it intersects with a safe set to get a safe reachable set. The safe set is defined by constraints of positive signed distances for obstacles in the environment and computed by solving QP optimization problems offline. For states inside the intersection set, i.e., the safe reachable set, the computed backward reachable tube ensures they are reachable subjected to system dynamics and input bounds, and the safe set guarantees they satisfy parking safety with respect to obstacles in different shapes. For online computation, randomized states are sampled from the safe reachable set, and used as heuristic guide points to be considered in the bidirectional A* search. The bidirectional A* search is paralleled for each randomized state from the safe reachable set. We show that the proposed two-level planning algorithm is able to solve different parking scenarios effectively and computationally fast for typical parking requests. We validate our algorithm through simulations in large-scale randomized parking scenarios and demonstrate it to be able to outperform other state-of-the-art parking planning algorithms.

Geometric Projectors: Geometric Constraints based Optimization for Robot Behaviors

Generating motion for robots that interact with objects of various shapes is a complex challenge, further complicated when the robot's own geometry and multiple desired behaviors are considered. To address this issue, we introduce a new framework based on Geometric Projectors (GeoPro) for constrained optimization. This novel framework allows for the generation of task-agnostic behaviors that are compliant with geometric constraints. GeoPro streamlines the design of behaviors in both task and configuration spaces, offering diverse functionalities such as collision avoidance and goal-reaching, while maintaining high computational efficiency. We validate the efficacy of our work through simulations and Franka Emika robotic experiments, comparing its performance against state-of-the-art methodologies. This comprehensive evaluation highlights GeoPro's versatility in accommodating robots with varying dynamics and precise geometric shapes. For additional materials, please visit: https://www.xueminchi.com/publications/geopro

Obstacle Avoidance for Unicycle-Modelled Mobile Robots with Time-varying Control Barrier Functions

In this paper, we propose a safety-critical controller based on time-varying control barrier functions (CBFs) for a robot with an unicycle model in the continuous-time domain to achieve navigation and dynamic collision avoidance. Unlike previous works, our proposed approach can control both linear and angular velocity to avoid collision with obstacles, overcoming the limitation of confined control performance due to the lack of control variable. To ensure that the robot reaches its destination, we also design a control Lyapunov function (CLF). Our safety-critical controller is formulated as a quadratic program (QP) optimization problem that incorporates CLF and CBFs as constraints, enabling real-time application for navigation and dynamic collision avoidance. Numerical simulations are conducted to verify the effectiveness of our proposed approach.

Velocity Obstacle for Polytopic Collision Avoidance for Distributed Multi-robot Systems

Obstacle avoidance for multi-robot navigation with polytopic shapes is challenging. Existing works simplify the system dynamics or consider it as a convex or non-convex optimization problem with positive distance constraints between robots, which limits real-time performance and scalability. Additionally, generating collision-free behavior for polytopic-shaped robots is harder due to implicit and non-differentiable distance functions between polytopes. In this paper, we extend the concept of velocity obstacle (VO) principle for polytopic-shaped robots and propose a novel approach to construct the VO in the function of vertex coordinates and other robot's states. Compared with existing work about obstacle avoidance between polytopic-shaped robots, our approach is much more computationally efficient as the proposed approach for construction of VO between polytopes is optimization-free. Based on VO representation for polytopic shapes, we later propose a navigation approach for distributed multi-robot systems. We validate our proposed VO representation and navigation approach in multiple challenging scenarios including large-scale randomized tests, and our approach outperforms the state of art in many evaluation metrics, including completion rate, deadlock rate, and the average travel distance.

Optimization-Based Motion Planning for Autonomous Parking Considering Dynamic Obstacle: A Hierarchical Framework

We present a hierarchical framework based on graph search and model predictive control (MPC) for electric autonomous vehicle (EAV) parking maneuvers in a tight environment. At high-level, only static obstacles are considered, and the scenario-based hybrid A* (SHA*), which is faster than the traditional hybrid A*, is designed to provide an initial guess (also known as a global path) for the parking task. To extract the velocity and acceleration profile from an initial guess, an optimal control problem (OCP) is built. At the low level, an NMPC-based strategy is used to avoid dynamic obstacles (also known as local planning). The efficacy of SHA* is evaluated through 148 different simulation schemes and the proposed hierarchical parking framework is demonstrated through a real-time parallel parking simulation.

Search-Based Path Planning Algorithm for Autonomous Parking:Multi-Heuristic Hybrid A*

This paper proposed a novel method for autonomous parking. Autonomous parking has received a lot of attention because of its convenience, but due to the complex environment and the non-holonomic constraints of vehicle, it is difficult to get a collision-free and feasible path in a short time. To solve this problem, this paper introduced a novel algorithm called Multi-Heuristic Hybrid A* (MHHA*) which incorporates the characteristic of Multi-Heuristic A* and Hybrid A*. So it could provide the guarantee for completeness, the avoidance of local minimum and sub-optimality, and generate a feasible path in a short time. And this paper also proposed a new collision check method based on coordinate transformation which could improve the computational efficiency. The performance of the proposed method was compared with Hybrid A* in simulation experiments and its superiority has been proved.