Bi-objective Motion Planning Approach for Safe Motions: Application to a Collaborative Robot

Abstract

This paper presents a new bi-objective safety-oriented path planning strategy for robotic manipulators. Integrated into a sampling-based algorithm, our approach can successfully enhance the task safety by guiding the expansion of the path towards the safest configurations. Our safety notion consists of avoiding dangerous situations, e.g. being very close to the obstacles, human awareness, e.g. being as much as possible in the human vision field, as well as ensuring human safety by being as far as possible from human with hierarchical priority between human body parts. Experimental validations are conducted in simulation and on the real Baxter research robot. They revealed the efficiency of the proposed method, mainly in the case of a collaborative robot sharing the workspace with humans.

Appendix A: Bisection Continuous Collision Checking Method

In this section, we give an overview of the modified bisection continuous collision checking method [17], which can efficiently handle the case of spherical and two revolute joints by providing tight motion bounds, thus increasing the success rate of checking collision-free paths. Collision checking is an essential step in motion planning as it ensures the path to be collision-free. The main challenge relies on determining whether the continuous path between two states in C-space is in collision or not. Bisection collision checking method [44] is one of the Continuous Collision Detection (CCD) methods, the main idea behind this method is to establish a sufficient condition of collision-free by computing the geometric path of rigid bodies in the workspace (Fig. 20). A sufficient condition to guarantee that two rigid objects, A₁ and A₂, do not collide at any configuration q located on the path segment π, which is joining two configurations q_a and q_b, is to verify the following inequality:

$$ \lambda_{1}(q_{a},q_{b})+\lambda_{2}(q_{a},q_{b})<\eta_{12}(q_{a})+\eta_{12}(q_{b}) $$

(10)

where η₁₂(q_i) is the minimum distance between objects A₁ and A₂ for a given configuration q_i, and λ_i(q_a,q_b) refers to the maximum Euclidean displacement of all the points in object i along the path segment π.

Fig. 20

Example: Two types of collision analysis for a 3-DOF robotic arm

If A₁ is a link of the robot and A₂ is a fixed obstacle, we define the estimated clearance for a path between two configurations q_a and q_b as follows:

$$ \begin{aligned} \delta &=\frac{\eta_{12}(q_{a})+\eta_{12}(q_{b})-\lambda_{1}(q_{a},q_{b})}{2}\\ {}&=dist(q_{a},q_{b},A_{1},A_{2}) \end{aligned} $$

(11)

The procedure to compute the minimum clearance along a path segment and sorting collision-free segment paths according to their clearance is given in Algorithm 4. Note that each element of the structure segment refers to a specific pair of link/obstacle evaluated between two states and is used to store the corresponding distance information. Parameter 𝜖 can be defined as the maximum admissible error in the distance estimation. It is a positive user-defined constant that affects the performances of the algorithm: decreasing it improves the returned distance estimation accuracy whereas increasing it reduces the required computational burden to generate the estimation.

The estimated and exact distances to obstacles satisfy the following inequality:

$$ \delta_{exa} -\frac{\epsilon}{2}\leq\ \delta\leq \delta_{exa} $$

(12)

where δ_exa and δ are, respectively, the exact and estimated minimum distances between two objects A₁ and A₂, where A₁ moves from configuration q_a to q_b and A₂ is a fixed obstacle.